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Related papers: Transient analysis of the Erlang A model

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In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…

Probability · Mathematics 2016-01-13 Joke Blom , Koen de Turck , Michel Mandjes

This paper considers a modified Erlang loss system for cognitive wireless networks and related applications. A primary user has preemptive priority over secondary users and the primary customer is lost if upon arrival all the channels are…

Performance · Computer Science 2021-03-05 E. V. Morozov , S. S. Rogozin , H. Q. Nguyen , T. Phung-Duc

In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is…

Dynamical Systems · Mathematics 2022-11-23 Philip Doldo , Jamol Pender

Approximations for the mean performance indices for the M/G/c queue rely on the approximate computation of the probability that an arriving request has to wait for service and of the minimum of residual service times if all servers are…

Networking and Internet Architecture · Computer Science 2008-03-14 Thomas Begin , Alexandre Brandwajn

We consider a system consisting of a server alternating between two service points. At both service points there is an infinite queue of customers that have to undergo a preparation phase before being served. We are interested in the…

Probability · Mathematics 2014-04-23 Maria Vlasiou , Ivo J. B. F. Adan

In the infinite servers queue with Poisson arrivals real life practical applications, the busy period and the busy cycle probabilistic study is of main importance. But it is a very difficult task. In this text, we show that by solving a…

Probability · Mathematics 2022-04-05 Manuel Alberto M. Ferreira

We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth and death like transitions, for which it is shown that for any state $i$, the rate of two…

Probability · Mathematics 2015-10-12 Binyamin Oz , Ivo Adan , Moshe Haviv

We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of…

Probability · Mathematics 2023-07-19 Sonja Otten , Ruslan Krenzler , Hans Daduna , Karsten Kruse

Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…

Statistics Theory · Mathematics 2025-10-24 Attila Lovas

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded- volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state…

Statistical Mechanics · Physics 2014-09-18 Chikashi Arita

In this paper, we analyze a multiserver Markovian queue with customer abandonment i.e. the Erlang-A queue uder a novel framework, i.e. the random impulsive differential equations (RIDEs). This framework captures systems that evolve…

Probability · Mathematics 2026-03-17 Ruici Gao , Jamol Pender

This paper presents a method for calculating steady state probabilities of $M|E_r|c|K$ queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this…

Systems and Control · Computer Science 2014-01-21 Stefan Hochrainer , Ronald Hochreiter , Georg Pflug

In many cognitive radio applications, there are multiple types of message queues. Existing queueing analysis works in underlay CR networks failed to discuss packets heterogeneity. Therefore high priority packets with impatient waiting time…

Networking and Internet Architecture · Computer Science 2017-06-27 Long Chen , Liusheng Huang , Hongli Xu , Jie Hu

Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…

Networking and Internet Architecture · Computer Science 2015-06-16 Nico Becker , Markus Fidler

A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…

Probability · Mathematics 2011-08-05 Samantha Molinaro , Myron Hlynka , Shan Xu

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling…

Statistical Mechanics · Physics 2009-11-10 Meesoon Ha , Jussi Timonen , Marcel den Nijs

A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…

Probability · Mathematics 2014-01-17 Yunan Liu , Ward Whitt

We study in this paper an $M/M/1$ queue whose server rate depends upon the state of an independent Ornstein-Uhlenbeck diffusion process $(X(t))$ so that its value at time $t$ is $\mu \phi(X(t))$, where $\phi(x)$ is some bounded function and…

Networking and Internet Architecture · Computer Science 2008-12-16 Christine Fricker , Fabrice Guillemin , Philippe Robert

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience…

Probability · Mathematics 2013-08-27 Jiheng Zhang

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers…

Probability · Mathematics 2014-01-22 Xin Liu , Qi Gong , Vidyadhar G. Kulkarni