ORCID Profile
0000-0001-7600-5383
Current Organisations
Yantai University
,
University of Melbourne
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Statistics | Stochastic Analysis and Modelling | Stochastic Analysis And Modelling | Operations Research | Applied Mathematics | Operations Research | Dynamical Systems | Wildlife and Habitat Management | Broadband Network Technology | Mathematical Physics | Systems Theory And Control | Optimisation | Computer Communications Networks | Applied Statistics | Optimisation | Communications Technologies | Statistical Theory | Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matter | Mathematical Sciences Not Elsewhere Classified | Mining Engineering | Conservation and Biodiversity | Health Information Systems (incl. Surveillance) | Thermodynamics And Statistical Physics |
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Mathematical Sciences | Mathematical sciences | Telecommunications | Education and training not elsewhere classified | Ecosystem Assessment and Management at Regional or Larger Scales | Technological and Organisational Innovation | Public Health (excl. Specific Population Health) not elsewhere classified | Coal | Network switching equipment | Network transmission equipment | Health policy evaluation | Expanding Knowledge in the Medical and Health Sciences | Energy Services and Utilities | Urban and Industrial Water Management | Atmospheric processes | Industrial Energy Conservation and Efficiency | Other | Expanding Knowledge in the Environmental Sciences | Flora, Fauna and Biodiversity at Regional or Larger Scales
Related Links
Publications
On the inverse of Erlang's function
Publisher: Cambridge University Press (CUP)
Date: 03-1998
DOI: 10.1017/S0021900200014856
Abstract: Erlang's function B (λ, C ) gives the blocking probability that occurs when Poisson traffic of intensity λ is offered to a link consisting of C circuits. However, when dimensioning a telecommunications network, it is more convenient to use the inverse C (λ, B ) of Erlang's function, which gives the number of circuits needed to carry Poisson traffic λ with blocking probability at most B . This paper derives simple bounds for C (λ, B ). These bounds are close to each other and the upper bound provides an accurate linear approximation to C (λ, B ) which is asymptotically exact in the limit as λ approaches infinity with B fixed
Maximal Profit Dimensioning and Tariffing of Loss Networks
Publisher: Cambridge University Press (CUP)
Date: 07-1995
DOI: 10.1017/S0269964800003909
Abstract: In this paper we present a unified approach to the optimal dimensioning and tariffing of loss networks. In our formulation the optimum is chosen to maximize the profit for the company operating the loss network. We assume that the operating company has the flexibility to determine tariffs and grade of service — although both of these can possibly be subject to regulatory constraints. The fact that the tariffing may affect demand and, hence, the dimensioning makes it essential that the operating company include the tariff/demand trade-off in determining the optimal way to dimension the loss network. A consequence of our formulation is that the optimal tariff structure has a particularly simple form, with the optimal tariff on a particular route separating into a term related to the tariff/demand trade-off on that route and a term that reflects the cost of the circuits used by the route.
The design of ATM virtual path connection networks with service separation
Publisher: IEEE Comput. Soc
Date: 2000
Modeling handovers in cellular mobile networks with dynamic channel allocation
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 02-1995
DOI: 10.1287/OPRE.43.1.33
Abstract: A model for a cellular mobile network is given which uses the dynamic channel allocation strategy proposed by Everitt and Macfadyen (Everitt, D. E., N. W. Macfadyen. 1983. Analysis of multicellular mobile radiotelephone systems with loss. British Telecom. Tech. J. 137–45.). In this model, handovers of calls from one cell to another are explicitly included. The equilibrium distribution of this network is shown to have product form under certain reversibility conditions. The conditions are restrictive and are, perhaps, unlikely to hold in practical models. However, their study does provide insight into the behavior of cellular systems with dynamic channel allocation. Using the product-form equilibrium distribution we are able to express the blocking probability for new calls, and the blocking probability for handover calls in terms of appropriate normalizing constants. The model is also extended to allow directed retry for handovers in which blocked handover attempts may try to gain access via another cell. This provides differential service for handovers. Again, some reversibility conditions ensure product form, and the blocking probabilities for both new and handover calls are given in terms of normalizing constants.
Hitting probabilities and hitting times for stochastic fluid flows: The bounded model
Publisher: Cambridge University Press (CUP)
Date: 13-11-2009
DOI: 10.1017/S0269964809000102
Abstract: We consider a Markovian stochastic fluid flow model in which the fluid level has a lower bound zero and a positive upper bound. The behavior of the process at the boundaries is modeled by parameters that are different than those in the interior and allow for modeling a range of desired behaviors at the boundaries. We illustrate this with ex les. We establish formulas for several time-dependent performance measures of significance to a number of applied probability models. These results are achieved with techniques applied within the fluid flow model directly. This leads to useful physical interpretations, which are presented.
A stochastic analysis of a greedy routing scheme in sensor networks
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/080725684
Transient product from distributions in queueing networks
Publisher: Springer Science and Business Media LLC
Date: 09-1993
DOI: 10.1007/BF01439160
Pressure-driven variations of hydrogen bonding energy in ammonium azide (NH4N3): IR absorption and Raman scattering studies
Publisher: AIP Publishing
Date: 09-07-2014
DOI: 10.1063/1.4886184
Abstract: In this study, high pressure infrared (IR) absorption and Raman scattering studies for ammonium azide (NH4N3) were carried out at room temperature up to 20 GPa and 22 GPa, respectively. For comparison and further assignment, the vibrational spectra at ambient conditions were calculated using CASTEP code, particularly for the far- and mid-IR modes. The recorded vibrational data consistently indicated a pressure-induced phase transition at 2.9 GPa. All observed vibrational modes maintained their identities at the high pressure phase, indicating that NH4N3 was still presented in the form of ammonium cations and azide anions linked by the hydrogen bond (N–H⋯N). Above 2.9 GPa, the relative magnitude of the torsional mode weakened and the N−H symmetric stretch displayed a redshift, indicating strengthened hydrogen bonding energy. The opposite effects were observed above 12 GPa, where the relative magnitude of the torsional mode strengthened and the N−H symmetric stretch reverted to a blueshift, indicating weakened hydrogen bonding energy. It can be concluded that the hydrogen bonding energy exhibited a weakening (0–2.9 GPa), strengthening (2.9–12 GPa), and then again weakening (12–22 GPa) phenomena with the increasing of compression. The hydrogen bonding energy changing with the increase of pressure can be ascribed to a phase transition at 2.9 GPa and a rotational or bending behavior of azide ions at 12 GPa.
Queues with advanced reservations: An infinite-server proxy for the bookings diary
Publisher: Cambridge University Press (CUP)
Date: 03-2016
DOI: 10.1017/APR.2015.4
Abstract: Queues with advanced reservations are endemic in the real world. In such a queue, the 'arrival' process is an incoming stream of customer 'booking requests', rather than actual customers requiring immediate service. We consider a model with a Poisson booking request process with rate λ. Associated with each request is a pair of independent random variables ( R i , S i ) constituting a request for service over a period S i , starting at a time R i into the future. Our interest is in the probability that a customer will be rejected due to capacity constraints. We present a simulation of a finite-capacity queue in which we record the proportion of rejected customers, and then move to an analysis of a queue with infinitely-many servers. Obviously no customers are rejected in the latter case. However, the event that the arrival of the extra customer will cause the number of customers in the queue to exceed C at some point during its service can be used as a proxy for the event that the customer would have been rejected in a system with finite capacity C . We start by calculating the transient and stationary distributions for some performance measures for the infinite-server queue. By observing that the stationary measure for the bookings diary (that is, the list of customers currently on hand, together with their start times and service times) is the same as the law for the entire s le path of an infinite server queue with a specified nonhomogenous Poisson input process, which we call the bookings queue , we are able to write down expressions for the abovementioned probability that, at some time during a requested service, the number of customers exceeds C . This measure serves as a bound for the probability that an incoming arrival would be refused admission in a system with C servers and, for a well-dimensioned system, it is to be hoped that it is a good approximation. We test the quality of this approximation by comparing our analytical results for the infinite-server case against simulation results for the finite-server case.
Incorporating Uncertainty of Management Costs in Sensitivity Analyses of Matrix Population Models
Publisher: Wiley
Date: 10-01-2013
DOI: 10.1111/COBI.12007
Abstract: The importance of accounting for economic costs when making environmental-management decisions subject to resource constraints has been increasingly recognized in recent years. In contrast, uncertainty associated with such costs has often been ignored. We developed a method, on the basis of economic theory, that accounts for the uncertainty in population-management decisions. We considered the case where, rather than taking fixed values, model parameters are random variables that represent the situation when parameters are not precisely known. Hence, the outcome is not precisely known either. Instead of maximizing the expected outcome, we maximized the probability of obtaining an outcome above a threshold of acceptability. We derived explicit analytical expressions for the optimal allocation and its associated probability, as a function of the threshold of acceptability, where the model parameters were distributed according to normal and uniform distributions. To illustrate our approach we revisited a previous study that incorporated cost-efficiency analyses in management decisions that were based on perturbation analyses of matrix population models. Incorporating derivations from this study into our framework, we extended the model to address potential uncertainties. We then applied these results to 2 case studies: management of a Koala (Phascolarctos cinereus) population and conservation of an olive ridley sea turtle (Lepidochelys olivacea) population. For low aspirations, that is, when the threshold of acceptability is relatively low, the optimal strategy was obtained by ersifying the allocation of funds. Conversely, for high aspirations, the budget was directed toward management actions with the highest potential effect on the population. The exact optimal allocation was sensitive to the choice of uncertainty model. Our results highlight the importance of accounting for uncertainty when making decisions and suggest that more effort should be placed on understanding the distributional characteristics of such uncertainty. Our approach provides a tool to improve decision making.
On the dual relationship between markov chains of GI/M/1 and M/G/1 type
Publisher: Cambridge University Press (CUP)
Date: 03-2010
Abstract: In 1990, Ramaswami proved that, given a Markov renewal process of M/G/1 type, it is possible to construct a Markov renewal process of GI/M/1 type such that the matrix transforms G ( z , s ) for the M/G/1-type process and R ( z , s ) for the GI/M/1-type process satisfy a duality relationship. In his 1996 PhD thesis, Bright used time reversal arguments to show that it is possible to define a different dual for positive-recurrent and transient processes of M/G/1 type and GI/M/1 type. Here we compare the properties of the Ramaswami and Bright dual processes and show that the Bright dual has desirable properties that can be exploited in the design of algorithms for the analysis of Markov chains of GI/M/1 type and M/G/1 type.
Truncation and augmentation of level-independent QBD processes
Publisher: Elsevier BV
Date: 05-2002
Predicting overflow in an emergency department
Publisher: Oxford University Press (OUP)
Date: 22-08-2009
Approximation of performance measures in cellular mobile networks with dynamic channel allocation
Publisher: Springer Science and Business Media LLC
Date: 06-1994
DOI: 10.1007/BF02110140
Triggered batch movement in queueing networks
Publisher: Springer Science and Business Media LLC
Date: 03-1995
DOI: 10.1007/BF01158577
A report from the International mathematical union (IMU) in cooperation with the International council of industrial and applied mathematics (ICIAM) and the institute of mathematical statistics (IMS)
Publisher: Institute of Mathematical Statistics
Date: 02-2009
DOI: 10.1214/09-STS285
Comments on: Light tail asymptotics in multidimensional reflecting processes for queueing networks
Publisher: Springer Science and Business Media LLC
Date: 19-04-2011
Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework
Publisher: Cold Spring Harbor Laboratory
Date: 17-09-2022
DOI: 10.1101/2022.09.14.22279950
Abstract: Most disease pathogens require onward transmission for their continued persistence. It is necessary to have continuous replenishment of the population of susceptibles, either through births, immigration, or waning immunity in recovered in iduals. Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an in idual recovers. If the disease takes off, the number of infectives will typically decrease to a low level after the first major outbreak. During this period, the disease dynamics will be highly influenced by stochastic effects and there is a non-zero probability that the epidemic will die out. This is known as an epidemic fade-out. If the disease does not die out, the susceptible population may be replenished by the waning of immunity, and a second wave may start. In this study, we describe an experiment where we generated synthetic outbreak data from independent stochastic SIRS models in multiple communities. Some of the outbreaks faded-out and some did not. By conducting Bayesian parameter estimation independently on each outbreak, as well as under a hierarchical framework, we investigated if the waning immunity rate could be correctly identified. When the outbreaks were considered independently, the waning immunity rate was incorrectly estimated when an epidemic fade-out was observed. However, the hierarchical approach improved the parameter estimates. This was particularly the case for those communities where the epidemic faded out.
How old is this bird? The age distribution under some phase sampling schemes
Publisher: Springer Science and Business Media LLC
Date: 03-04-2017
DOI: 10.1007/S00285-017-1121-X
Abstract: In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an in idual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the in idual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during the monitoring period 2007-2014.
A Restless Bandit Model for Resource Allocation, Competition, and Reservation
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 2022
Abstract: In “A Restless Bandit Model for Resource Allocation, Competition and Reservation,” J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s idea of relaxing the constraints and Weber and Weiss’s proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case.
A paradox for expected hitting times
Publisher: Informa UK Limited
Date: 02-03-2020
Strategic customer behavior in an M/M/1 feedback queue
Publisher: Springer Science and Business Media LLC
Date: 20-03-2021
The time-dependent expected reward and deviation matrix of a finite QBD process
Publisher: Elsevier BV
Date: 06-2019
On the problem of establishing the existence of stationary distributions for continuous-time markov chains
Publisher: Cambridge University Press (CUP)
Date: 10-1993
DOI: 10.1017/S0269964800003119
Abstract: We consider the problem of establishing the existence of stationary distributions for continuous-time Markov chains directly from the transition rates Q . Given an invariant probability distribution m for Q , we show that a necessary and sufficient condition for m to be a stationary distribution for the minimal process is that Q be regular. We provide sufficient conditions for the regularity of Q that are simple to verify in practice, thus allowing one to easily identify stationary distributions for a variety of models. To illustrate our results, we shall consider three classes of multidimensional Markov chains, namely, networks of queues with batch movements, semireversible queues, and partially balanced Markov processes.
Dynamic reallocation of capacity in logically fully-connected networks
Publisher: Wiley
Date: 2004
DOI: 10.1002/NEM.499
Drift conditions for matrix-analytic models
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 05-2003
DOI: 10.1287/MOOR.28.2.346.14475
Abstract: In his seminal work, Neuts gave drift criteria by which one can determine whether processes of GI/M/1 or M/G/1 type are positive recurrent. Recently, a different drift condition to determine the ergodic character of a quasi-birth-and-death process (QBD) appeared in the literature, although its justification does not seem to have been formally established. In this paper, we provide a proof for this new drift condition in a general context. We also give a simple proof for Neuts' original condition and establish a number of new drift conditions for the ergodic character of matrix-analytic models.
Level-phase independent stationary distributions for GI/M/1-type Markov chains with infinitely-many phases
Publisher: Elsevier BV
Date: 09-2013
Algorithms for return probabilities for stochastic fluid flows
Publisher: Informa UK Limited
Date: 09-02-2005
Combination Load Balancing for Video-on-Demand Systems
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 07-2008
Safe Blues: The case for virtual safe virus spread in the long-term fight against epidemics
Publisher: Elsevier BV
Date: 03-2021
Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes
Publisher: Informa UK Limited
Date: 1995
Mean-value analysis for a class of Petri nets and batch-movement queueing networks with product-form equilibrium distributions
Publisher: Elsevier BV
Date: 11-1995
Transient Markov arrival processes
Publisher: Institute of Mathematical Statistics
Date: 05-2003
A spot welding reliability problem
Publisher: Elsevier BV
Date: 1987
Cost-effective deployment of bandwidth partitioning in broadband networks
Publisher: Springer Science and Business Media LLC
Date: 2004
Procrustes based metrics for spatial validation and calibration of two-dimensional perimeter spread models: A case study considering fire
Publisher: Elsevier BV
Date: 07-2012
Proof of the Hamiltonicity-trace conjecture for singularly perturbed Markov chains
Publisher: Cambridge University Press (CUP)
Date: 12-2011
Abstract: We prove the conjecture formulated in Litvak and Ejov (2009), namely, that the trace of the fundamental matrix of a singularly perturbed Markov chain that corresponds to a stochastic policy feasible for a given graph is minimised at policies corresponding to Hamiltonian cycles.
Characterization of matrix-exponential distributions
Publisher: Informa UK Limited
Date: 08-2008
A correspondence between product-form batch-movement queueing networks and single-movement networks
Publisher: Cambridge University Press (CUP)
Date: 03-1997
DOI: 10.1017/S0021900200100798
Abstract: A number of recent papers have exhibited classes of queueing networks, with batches of customers served and routed through the network, which have generalised product-form equilibrium distributions. In this paper we look at these from a new viewpoint. In particular we show that, under standard assumptions, for a network to possess an equilibrium distribution that factorises into a product form over the nodes of the network for all possible transition rates, it is necessary and sufficient that it be equivalent to a suitably-defined single-movement network. We consider also the form of the state space for such networks.
A lightning-caused wildfire ignition forecasting model for operational use
Publisher: Elsevier BV
Date: 05-2018
Why is Kemeny's constant a constant?
Publisher: Cambridge University Press (CUP)
Date: 12-2018
DOI: 10.1017/JPR.2018.68
Abstract: In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as Kemeny’s constant . Various proofs have been given over time, some more technical than others. We give here a very simple physical justification, which extends without a hitch to continuous-time Markov chains on a finite state space. For Markov chains with denumerably infinite state space, the constant may be infinite and even if it is finite, there is no guarantee that the physical argument will hold. We show that the physical interpretation does go through for the special case of a birth-and-death process with a finite value of Kemeny’s constant.
The value of communication and cooperation when servers are strategic
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 06-05-2020
DOI: 10.21914/ANZIAMJ.V61I0.14157
Abstract: In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability one of the two servers is always inactive each server knows the other’s successful transmission probability and they are willing to cooperate. Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate (II) neither communicate nor cooperate (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III. doi:10.1017/S1446181120000048
A two-time-scale model for hospital patient flow
Publisher: Oxford University Press (OUP)
Date: 07-2005
What is a unit of capacity worth?
Publisher: Cambridge University Press (CUP)
Date: 10-2002
DOI: 10.1017/S0269964802164084
Abstract: Consider a finite-capacity telecommunications link to which connection requests arrive in a Poisson process. Each connection carried on the link earns a certain amount of revenue for the link's manager. Now, assume that the manager is offered the opportunity to buy or sell a unit of the link's allocated capacity. Assuming that the manager has a knowledge of the current number of connections on the link, we demonstrate a method of calculating the buying and selling prices.
Quasistationary distributions for level-dependent quasi-birth-and-death processes
Publisher: Informa UK Limited
Date: 2000
Bounds for the solution to the single-period inventory model with compound renewal process input: An application to setting credit card limits
Publisher: Elsevier BV
Date: 05-2019
The Markov-modulated Erlang loss system
Publisher: Elsevier BV
Date: 11-2017
Woody species diversity influences productivity and soil nutrient availability in tropical plantations
Publisher: Springer Science and Business Media LLC
Date: 27-09-2007
DOI: 10.1007/S00442-007-0850-8
Abstract: We investigated the relationship between plant ersity and ecological function (production and nutrient cycling) in tropical tree plantations. Old plantations (65-72 years) of four different species, namely Araucaria cunninghamii, Agathis robusta, Toona ciliata and Flindersia brayleyana, as well as natural secondary forest were examined at Wongabel State Forest, in the wet tropics region of Queensland, Australia. Two young plantations (23 years) of Araucaria cunninghamii and Pinus caribaea were also examined. The close proximity of the older plantations and natural forests meant they had similar edaphic and climatic conditions. All plantations had been established as monocultures, but had been colonised by a range of native woody plants from the nearby rainforest. The extent to which this had occurred varied with the identity of the plantation species (from 2 to 17 species in 0.1 ha blocks). In many cases these additional species had grown up and joined the forest canopy. This study is one of the few to find a negative relationship between overstorey plant ersity and productivity. The conversion of natural forest with highly productive, low- ersity gymnosperm-dominated plantations (young and old Araucaria cunninghamii and Pinus caribaea) was found to be associated with lower soil nutrient availability (approximately five times less phosphorus and 2.5 times less nitrogen) and lower soil pH (mean=6.28) compared to the other, less productive plantations. The dominant effects of two species, Araucaria cunninghamii and Hodgkinsonia frutescens, indicate that ecosystem functions such as production and nutrient availability are not determined solely by the number of species, but are more likely to be determined by the characteristics of the species present. This suggests that monoculture plantations can be used to successfully restore some functions (e.g. nutrient cycling and production), but that the level to which such functions can be restored will depend upon the species chosen and site conditions.
The paradox of Parrondo's games
Publisher: The Royal Society
Date: 08-02-2000
A sequential stochastic mixed integer programming model for tactical master surgery scheduling
Publisher: Elsevier BV
Date: 10-2018
Markovian trees: Properties and algorithms
Publisher: Springer Science and Business Media LLC
Date: 06-12-2008
Optimal market thickness
Publisher: Elsevier BV
Date: 03-2022
The algebraic degree of phase-type distributions
Publisher: Cambridge University Press (CUP)
Date: 09-2010
Abstract: This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.
THE VALUE OF COMMUNICATION AND COOPERATION WHEN SERVERS ARE STRATEGIC
Publisher: Cambridge University Press (CUP)
Date: 10-2019
DOI: 10.1017/S1446181120000048
Abstract: In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability one of the two servers is always inactive each server knows the other’s successful transmission probability and they are willing to cooperate. Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate (II) neither communicate nor cooperate (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III.
Performance Analysis of Resource Selection Schemes for a Large Scale Video-on-Demand System
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2008
Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework
Publisher: Elsevier BV
Date: 12-2023
On the inverse of Erlang’s function
Publisher: Cambridge University Press (CUP)
Date: 03-1998
Abstract: Erlang's function B (λ, C ) gives the blocking probability that occurs when Poisson traffic of intensity λ is offered to a link consisting of C circuits. However, when dimensioning a telecommunications network, it is more convenient to use the inverse C (λ, B ) of Erlang's function, which gives the number of circuits needed to carry Poisson traffic λ with blocking probability at most B . This paper derives simple bounds for C (λ, B ). These bounds are close to each other and the upper bound provides an accurate linear approximation to C (λ, B ) which is asymptotically exact in the limit as λ approaches infinity with B fixed
A general formulation for mean-value analysis in product-form batch-movement queueing networks
Publisher: Springer Science and Business Media LLC
Date: 09-1994
DOI: 10.1007/BF01158962
Level-phase independence for GI/M/1-Type Markov chains
Publisher: Cambridge University Press (CUP)
Date: 12-2000
Abstract: GI / M /1-type Markov chains make up a class of two-dimensional Markov chains. One dimension is usually called the level, and the other is often called the phase. Transitions from states in level k are restricted to states in levels less than or equal to k +1. For given transition probabilities in the interior of the state space, we show that it is always possible to define the boundary transition probabilities in such a way that the level and phase are independent under the stationary distribution. We motivate our analysis by first considering the quasi-birth-and-death process special case in which transitions from any state are restricted to states in the same, or adjacent, levels.
Quasi-reversibility and networks of queues with nonstandard batch movements
Publisher: Elsevier BV
Date: 05-2000
A multi-class multi-server accumulating priority queue with application to health care
Publisher: Elsevier BV
Date: 06-2014
Allocation in a vertical rotary car park
Publisher: Springer International Publishing
Date: 2017
Some properties of the capacity value function
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2005
A queueing model for the capacity planning of a multi-phase human services process
Publisher: Informa UK Limited
Date: 17-03-2015
Use of clustering to improve estimation of epidemic model parameters under a Bayesian hierarchical framework
Publisher: Cold Spring Harbor Laboratory
Date: 13-12-2022
DOI: 10.1101/2022.12.08.22283266
Abstract: We study infectious disease outbreaks that have evolved in isolation without the influence of one another. If stochastic effects are identified within each outbreak, it is necessary to model the dynamics with stochastic epidemic models. However, the accuracy of the estimated model parameters depends on several factors including the statistical inference methodologies that are used. One approach to making inferences from multiple outbreak data is the use of a Bayesian hierarchical model. This statistical framework allows simultaneous inference for multiple outbreaks and the estimation of model parameters at a group level. A hierarchical model will generally provide improved estimates however, we show that this is not always true when the variability among model parameter values of the outbreaks is high. We further show that subsets of outbreaks with similar parameter values can be identified prior to a hierarchical analysis using common clustering algorithms such as k-means. When hierarchical analyses are carried out for these pre-identified subsets of outbreaks, parameter estimates are improved compared to those estimated under a hierarchical analysis for the complete set of outbreaks. We have applied our estimation framework within a simulation-based experiment using synthetic data generated from stochastic SIRS models. The framework is generalizable to other biological data.
Decay rates for quasi-birth-and-death processes with countably many phases and tridiagonal block generators
Publisher: Cambridge University Press (CUP)
Date: 06-2006
Abstract: We consider the class of level-independent quasi-birth-and-death (QBD) processes that have countably many phases and generator matrices with tridiagonal blocks that are themselves tridiagonal and phase independent. We derive simple conditions for possible decay rates of the stationary distribution of the ‘level’ process. It may be possible to obtain decay rates satisfying these conditions by varying only the transition structure at level 0. Our results generalize those of Kroese, Scheinhardt, and Taylor, who studied in detail a particular ex le, the tandem Jackson network, from the class of QBD processes studied here. The conditions derived here are applied to three practical ex les.
A Model for Cell Proliferation in a Developing Organism
Publisher: Springer Science and Business Media LLC
Date: 06-2022
DOI: 10.1007/S00285-022-01769-5
Abstract: In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models governed by local stochastic rules. We discuss a particular ex le of this approach: a model for the proliferation of neural crest cells that can help us understand the development of Hirschprung’s disease, a potentially-fatal condition in which the enteric nervous system of a new-born child does not extend all the way through the intestine and colon. Our starting point is a discrete-state, continuous-time Markov chain model proposed by Hywood et al. (2013a) for the location of the neural crest cells that make up the enteric nervous system. Hywood et al. (2013a) scaled their model to derive an approximate second order partial differential equation describing how the limiting expected number of neural crest cells evolve in space and time. In contrast, we exploit the relationship between the above-mentioned Markov chain model and the well-known Yule-Furry process to derive the exact form of the scaled version of the process. Furthermore, we provide expressions for other features of the domain agent occupancy process, such as the variance of the marginal occupancy at a particular site, the distribution of the number of agents that are yet to reach a given site and a stochastic description of the process itself.
Decay rates for some quasi-birth-and-death processes with phase-dependent transition rates
Publisher: Cambridge University Press (CUP)
Date: 08-2011
Abstract: Recently, there has been considerable interest in the calculation of decay rates for models that can be viewed as quasi-birth-and-death (QBD) processes with infinitely many phases. In this paper we make a contribution to this endeavour by considering some classes of models in which the transition function is not homogeneous in the phase direction. We characterize the range of decay rates that are compatible with the dynamics of the process away from the boundary. In many cases, these rates can be attained by changing the transition structure of the QBD process at level 0. Our approach, which relies on the use of orthogonal polynomials, is an extension of that in Motyer and Taylor (2006) for the case where the generator has homogeneous blocks.
Waiting time distributions in the accumulating priority queue
Publisher: Springer Science and Business Media LLC
Date: 07-12-2013
Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 12-2017
Abstract: In 1964, Kleinrock proposed a queueing discipline for a single-server queue in which customers from different classes accumulate priority as linear functions of their waiting time. At the instant that a server becomes free, it selects the waiting customer with the highest accumulated priority, provided that the queue is nonempty. He developed a recursion for calculating the expected waiting time for each class. In 2014, Stanford, Taylor, and Ziedins reconsidered this queue, which they termed the accumulating priority queue (APQ), and derived the waiting time distribution for each class. Kleinrock and Finkelstein in 1967 also studied an accumulating priority system in which customers’ priorities increase as a power-law function of their waiting time. They established that it is possible to associate a particular linear APQ with such a power-law APQ, so that the expected waiting times of customers from all classes are preserved. In this paper, we extend their analysis to characterise the class of nonlinear APQs for which an equivalent linear APQ can be found, in the sense that, for identical s le paths of the arrival and service processes, the ordering of all customers is identical at all times in both the linear and nonlinear systems.
A stochastic fluid model for an ad hoc mobile network
Publisher: Springer Science and Business Media LLC
Date: 26-11-2009
Networks of interacting stochastic fluid models with infinite and finite buffers
Publisher: Springer Science and Business Media LLC
Date: 18-06-2019
How effective were Australian Quarantine Stations in mitigating transmission aboard ships during the influenza pandemic of 1918-19?
Publisher: Cold Spring Harbor Laboratory
Date: 18-01-2023
DOI: 10.1101/2023.01.13.23284542
Abstract: The influenza pandemic of 1918-19 was the most devastating pandemic of the 20th century. It killed an estimated 50–100 million people worldwide. In late 1918, when the severity of the disease was apparent, the Australian Quarantine Service was established. Vessels returning from overseas and inter-state were intercepted, and people were examined for signs of illness and quarantined. Some of these vessels carried the infection throughout their voyage and cases were prevalent by the time the ship arrived at a Quarantine Station. We study four outbreaks that took place on board the Medic, Boonah, Devon , and Manuka in late 1918. These ships had returned from overseas and some of them were carrying troops that served in the First World War. By analysing these outbreaks under a stochastic Bayesian hierarchical modeling framework, we estimate the transmission rates among crew and passengers aboard these ships. Furthermore, we ask whether the removal of infectious, convalescent, and healthy in iduals after arriving at a Quarantine Station in Australia was an effective public health response.
Two issues surrounding parrondo’s paradox
Publisher: Birkhäuser Boston
Date: 2005
Brownian ratchets and Parrondo's games
Publisher: AIP Publishing
Date: 31-08-2001
DOI: 10.1063/1.1395623
Abstract: Parrondo’s games present an apparently paradoxical situation where in idually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player’s current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of “noise” that is rectified by game B to produce overall positive drift—as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo’s games is that they are physically motivated and were originally derived by considering a Brownian ratchet—the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research.
On the dual relationship between Markov chains of GI/M/1 and M/G/1 type
Publisher: Cambridge University Press (CUP)
Date: 03-2010
DOI: 10.1017/S0001867800003979
Abstract: In 1990, Ramaswami proved that, given a Markov renewal process of M/G/1 type, it is possible to construct a Markov renewal process of GI/M/1 type such that the matrix transforms G ( z , s ) for the M/G/1-type process and R ( z , s ) for the GI/M/1-type process satisfy a duality relationship. In his 1996 PhD thesis, Bright used time reversal arguments to show that it is possible to define a different dual for positive-recurrent and transient processes of M/G/1 type and GI/M/1 type. Here we compare the properties of the Ramaswami and Bright dual processes and show that the Bright dual has desirable properties that can be exploited in the design of algorithms for the analysis of Markov chains of GI/M/1 type and M/G/1 type.
Renfrey Burnard Potts 1925-2005
Publisher: CSIRO Publishing
Date: 2014
DOI: 10.1071/HR14019
Abstract: Ren Potts was an Australian applied mathematician whose early work in statistical mechanics later became influential: the ‘Potts Model' became his most cited work. As Professor of Applied Mathematics at the University of Adelaide for thirty years, he built up an excellent Department of Mathematics and had a major influence on the development of Applied Mathematics in Australia. His work in transportation science and operations research is well known. Ren Potts was a gifted teacher and an inspiring research leader. He was an early advocate of close co-operation between academia and industry, was an early adopter of computing for research and teaching, and was a pioneer in forging new links between Australian universities and the South-East Asian region.
Modelling modal gating of ion channels with hierarchical Markov models
Publisher: The Royal Society
Date: 08-2016
Abstract: Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately representing activity changes is essential for accurately capturing time course data from ion channels, systematic approaches for modelling modal gating are currently not available. In this paper, we develop a modular approach for building such a model in an iterative process. First, stochastic switching between modes and stochastic opening and closing within modes are represented in separate aggregated Markov models. Second, the continuous-time hierarchical Markov model, a new modelling framework proposed here, then enables us to combine these components so that in the integrated model both mode switching as well as the kinetics within modes are appropriately represented. A mathematical analysis reveals that the behaviour of the hierarchical Markov model naturally depends on the properties of its components. We also demonstrate how a hierarchical Markov model can be parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlying molecular properties of the channel protein, it is likely that biophysical processes are better captured by our new approach than in earlier models.
The roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues
Publisher: Springer Science and Business Media LLC
Date: 11-04-2016
The distribution of the number of arrivals in a subinterval of a busy period of a single server queue
Publisher: Springer Science and Business Media LLC
Date: 07-2006
A general non-central hypergeometric distribution
Publisher: Informa UK Limited
Date: 24-05-2016
State-dependent coupling of quasireversible nodes
Publisher: Springer Science and Business Media LLC
Date: 2001
Geometric equilibrium distributions for queues with interactive batch departures
Publisher: Springer Science and Business Media LLC
Date: 10-1994
DOI: 10.1007/BF02033316
State-dependent coupling in general networks
Publisher: Springer Science and Business Media LLC
Date: 2001
A product-form 'loss network' with a form of queueing
Publisher: Cambridge University Press (CUP)
Date: 12-1997
DOI: 10.1017/S0021900200101755
Abstract: We show that a form of queueing can be introduced into the standard fixed-routing loss network model while retaining a product-form invariant measure.
THE RUNNING MAXIMUM OF A LEVEL-DEPENDENT QUASI-BIRTH-DEATH PROCESS
Publisher: Cambridge University Press (CUP)
Date: 21-12-2016
DOI: 10.1017/S026996481500039X
Abstract: The objective of this note is to study the distribution of the running maximum of the level in a level-dependent quasi-birth-death process. By considering this running maximum at an exponentially distributed “killing epoch” T , we devise a technique to accomplish this, relying on elementary arguments only importantly, it yields the distribution of the running maximum jointly with the level and phase at the killing epoch. We also point out how our procedure can be adapted to facilitate the computation of the distribution of the running maximum at a deterministic (rather than an exponential) epoch.
Algorithms for the Laplace-Stieltjes Transforms of first return times for stochastic fluid flows
Publisher: Springer Science and Business Media LLC
Date: 10-05-2008
Braess's paradox in a loss network
Publisher: Cambridge University Press (CUP)
Date: 03-1997
DOI: 10.1017/S0021900200100786
Abstract: Braess's paradox is said to occur in a network if the addition of an extra link leads to worse performance. It has been shown to occur in transportation networks (such as road networks) and also in queueing networks. Here, we show that it can occur in loss networks.
The output process of an MMPP/M/1 queue
Publisher: Cambridge University Press (CUP)
Date: 12-1998
Abstract: Olivier and Walrand (1994) claimed that the departure process of an MMPP/M/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. They also conjectured that the departure process of an MAP/PH/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. We show that their proof of the first result has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/M/1 can be an MAP.
A Convolution Algorithm for Calculating Exact Equilibrium Distributions in Resource Allocation Problems with Moderate User Interference
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 02-1994
A Markov analysis of social learning and adaptation
Publisher: Springer Science and Business Media LLC
Date: 04-2006
Evolutionary Optimization of File Assignment for a Large-Scale Video-on-Demand System
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 06-2008
The intercept term of the asymptotic variance curve for some queueing output processes
Publisher: Elsevier BV
Date: 04-2015
Reduced load approximations for loss networks
Publisher: Springer Science and Business Media LLC
Date: 12-1993
DOI: 10.1007/BF02109849
The spatial distribution of rainfall extremes and the influence of El Niño Southern Oscillation
Publisher: Elsevier BV
Date: 12-2017
Insensitivity in discrete time queues with a moving server
Publisher: Springer Science and Business Media LLC
Date: 09-1992
DOI: 10.1007/BF01164006
Discussion on “On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals,” by Jiandong Ren, Volume 12(2)
Publisher: Informa UK Limited
Date: 17-12-2015
Product form in networks of queues with batch arrivals and batch services
Publisher: Springer Science and Business Media LLC
Date: 12-1990
DOI: 10.1007/BF02411466
Rejoinder: Citation statistics
Publisher: Institute of Mathematical Statistics
Date: 02-2009
DOI: 10.1214/09-STS285REJ
Erratum: The distribution of the number of arrivals in a subinterval of a busy period of a single server queue (Queueing Systems (2006) 53 (105-114))
Publisher: Springer Science and Business Media LLC
Date: 06-2008
Random transmission radii in greedy routing models for ad hoc sensor networks
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/110823547
Algebraic criteria for extended product form in generalised semi-Markov processes
Publisher: Elsevier BV
Date: 09-1992
Queues with boundary assistance: The effects of truncation
Publisher: Springer Science and Business Media LLC
Date: 18-08-2011
Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals
Publisher: Springer Science and Business Media LLC
Date: 07-10-2023
An error bound for a continuous time approximation of discrete time servicing
Publisher: Informa UK Limited
Date: 1992
On the efficient use of video-on-demand storage facility
Publisher: IEEE
Date: 2003
Hitting probabilities and hitting times for stochastic fluid flows
Publisher: Elsevier BV
Date: 09-2005
Strong stochastic bounds for the stationary distribution of a class of multicomponent performability models
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
Date: 10-1998
Abstract: We consider a class of models for multicomponent systems in which components can break down and be repaired in a dependent manner and where breakdown and repair times can be arbitrarily distributed. The problem of calculating the equilibrium distribution and, from this, the expected performability for these models is intractable unless certain assumptions are made about breakdowns and repairs. In this paper we show that the performability of multicomponent systems that do not satisfy these rules can be bounded by tractable modifications. Our results are proved by stochastic comparability arguments and a Markov reward technique, which is of interest in itself as it enables one to prove that the equilibrium distribution of one process can be bounded by that of another even when the s le paths of the process are not. This is illustrated by an ex le.
Embedded processes in stochastic Petri nets
Publisher: No publisher found
Date: 1991
DOI: 10.1109/32.67592
Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay
Publisher: Elsevier BV
Date: 10-2016
An explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation
Publisher: Elsevier BV
Date: 05-2023
How do we encourage an egoist to act socially in an ad hoc mobile network?
Publisher: Elsevier BV
Date: 10-2012
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Publisher: Elsevier BV
Date: 09-1996
Maximal profit dimensioning and tariffing of loss networks with cross-connects
Publisher: Elsevier BV
Date: 05-2000
A model framework for greedy routing in a sensor network with a stochastic power scheme
Publisher: Association for Computing Machinery (ACM)
Date: 02-2011
Abstract: A stochastic model is formulated and analyzed to study the advancements of messages under greedy routing in a sensor network with a power-saving scheme. The aim of this model is give a better understanding of stochastic dependencies arising in the system and to offer a method of computing the advancement of message under greedy routing. We observe that the majority of the stochastic dependence from a routing path is captured by including only the previous forwarding node location. We examine a simple uncoordinated power-saving scheme with a new understanding of its effects on local node density. We propose a method for sensibly limiting the number of transmission reattempts before concluding there is no node in the forwarding region. All expressions involving multidimensional integrals are derived and evaluated readily with quasi-Monte Carlo integration methods. An importance s ling function is derived to speed up the quasi-Monte Carlo methods. The integral expressions are compared to simulations and give very agreeable results.
A distributed approach to capacity allocation in logical networks
Publisher: Elsevier BV
Date: 06-2010
Emulation of epidemics via Bluetooth-based virtual safe virus spread: Experimental setup, software, and data
Publisher: Public Library of Science (PLoS)
Date: 02-12-2022
DOI: 10.1371/JOURNAL.PDIG.0000142
Abstract: We describe an experimental setup and a currently running experiment for evaluating how physical interactions over time and between in iduals affect the spread of epidemics. Our experiment involves the voluntary use of the Safe Blues Android app by participants at The University of Auckland (UoA) City C us in New Zealand. The app spreads multiple virtual safe virus strands via Bluetooth depending on the physical proximity of the subjects. The evolution of the virtual epidemics is recorded as they spread through the population. The data is presented as a real-time (and historical) dashboard. A simulation model is applied to calibrate strand parameters. Participants’ locations are not recorded, but participants are rewarded based on the duration of participation within a geofenced area, and aggregate participation numbers serve as part of the data. The 2021 experimental data is available as an open-source anonymized dataset, and once the experiment is complete, the remaining data will be made available. This paper outlines the experimental setup, software, subject-recruitment practices, ethical considerations, and dataset description. The paper also highlights current experimental results in view of the lockdown that started in New Zealand at 23:59 on August 17, 2021. The experiment was initially planned in the New Zealand environment, expected to be free of COVID and lockdowns after 2020. However, a COVID Delta strain lockdown shuffled the cards and the experiment is currently extended into 2022.
Collective retention and transmission of chemical signals in a social insect
Publisher: Springer Science and Business Media LLC
Date: 12-02-2012
DOI: 10.1007/S00114-012-0891-7
Abstract: Social insect colonies exhibit highly coordinated responses to ecological challenges by acquiring information that is disseminated throughout the colony. Some responses are coordinated directly from the signals produced by in iduals that acquired the information. Other responses may require information to be transferred indirectly through a third party, thereby requiring colony-wide retention of information. Social insects use colony signature odours to distinguish between nestmates and non-nestmates, and the level of aggression between non-nestmates typically varies according to the distance between colonies and thus their history of interactions. Such coordinated, colony-specific responses may require information about particular odours to be disseminated and retained across the colony. Our field experiments with weaver ants reveal colony-wide, indirect acquisition and retention of the signature odours of a different colony with which they had experienced aggression. These data highlight the significance of interaction history and suggest the presence of a collective memory.
A comment on two-phase behavior of financial markets
Publisher: World Scientific Pub Co Pte Lt
Date: 02-2007
DOI: 10.1142/S0219024907004056
Abstract: A recent study linked the behavior of buying and selling in financial markets to the phenomenon of phase transitions that occur in physical systems with many interacting components. We urge caution with such findings. In particular, we show that the statistical technique employed in the study referred to above to analyze stock trading data also produces evidence of two-phase behavior when used to analyze a simple sequence of independent and identically distributed random variables.
Closed queueing networks with batch services
Publisher: Springer Science and Business Media LLC
Date: 12-1990
DOI: 10.1007/BF02411465
Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process
Publisher: Institute of Mathematical Statistics
Date: 11-2004
Annals of Operations Research: Preface
Publisher: Springer Science and Business Media LLC
Date: 19-01-2008
Insensitivity in stochastic models
Publisher: Springer US
Date: 15-11-2011
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