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In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a…

Probability · Mathematics 2018-05-02 David Koops , Mayank Saxena , Onno Boxma , Michel Mandjes

We study the Multiserver-Job Queuing Model (MJQM) with general independent arrivals and service times under FCFS scheduling, using stochastic recurrence equations (SREs) and ergodic theory. We prove the monotonicity and separability…

Performance · Computer Science 2026-01-29 Francois Baccelli , Diletta Olliaro , Marco Ajmone Marsan , Andrea Marin

We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an $M^{X}/G/1$ queue. Once the number of customers in the working mode drops…

Probability · Mathematics 2021-10-12 Igor Kleiner , Esther Frostig , David Perry

We study a queueing system with Erlang arrivals with $k$ phases and Erlang service with $m$ phases. Transition rates among phases vary periodically with time. For these systems, we derive the asymptotic periodic distribution of the level…

Probability · Mathematics 2021-07-29 Barbara Margolius

The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…

Probability · Mathematics 2018-12-07 Abhishek , Marko Boon , Rudesindo Núñez-Queija

In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss probability…

Probability · Mathematics 2012-05-01 Yuanyuan Liu , Yiqiang Zhao

We study a token-based central queue with multiple customer types. Customers of each type arrive according to a Poisson process and have an associated set of compatible tokens. Customers may only receive service when they have claimed a…

Probability · Mathematics 2019-02-07 U. Ayesta , T. Bodas , J. L. Dorsman , I. M. Verloop

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…

Probability · Mathematics 2008-08-01 Vyacheslav M. Abramov

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…

Networking and Internet Architecture · Computer Science 2021-08-05 Muthukrishnan Senthil Kumar , Aresh Dadlani , Kiseon Kim

The infinite servers queue with Poisson arrivals state transient probabilities, considering the time origin at the beginning of a busy period, mean and variance monotony as time functions is studied. These studies, for which results it is…

Probability · Mathematics 2021-09-29 Manuel Alberto M. Ferreira

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…

Probability · Mathematics 2017-05-02 Marko Boon , Onno Boxma , Offer Kella , Masakiyo Miyazawa

In this paper we study a two-queue polling model with zero switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$, $i=1,2$) in each queue. The arrival processes at the two queues are…

Probability · Mathematics 2019-02-20 Marko Boon , Erik Winands

We study the steady-state delay performance of load balancing in large-scale systems with heterogeneous servers in the heavy-traffic regimes. The system consists of $N$ servers, each with a local buffer of size $b-1$, serving jobs in the…

Probability · Mathematics 2026-02-27 Xin Liu , Lei Ying

Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…

Probability · Mathematics 2017-08-22 Harsha Honnappa , Rahul Jain

We consider sojourn or response times in processor-shared queues that have a finite population of potential users. Computing the response time of a tagged customer involves solving a finite system of linear ODEs. Writing the system in…

Probability · Mathematics 2013-09-12 Qiang Zhen , Charles Knessl

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service…

Classical Analysis and ODEs · Mathematics 2013-09-13 Qiang Zhen , Charles Knessl

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service…

Probability · Mathematics 2017-07-14 Mayank Saxena , Onno Boxma , Stella Kapodistria , Rudesindo Núñez Queija

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework, which was first introduced to derive the stability region for stochastic…

Probability · Mathematics 2017-11-29 Francois Baccelli , Sergey Foss

Motivated by the work of Whitt, who studied stabilization of the mean virtual waiting time (excluding service time) in a $GI_t/GI_t/1/FCFS$ queue, this paper investigates the stabilization of the mean virtual response time in a…

Performance · Computer Science 2020-09-09 Yongkyu Cho , Young Myoung Ko

We study a generalization of the $M/G/1$ system (denoted by $rM/G/1$) with independent and identically distributed (iid) service times and with an arrival process whose arrival rate $\lambda_0f(r)$ depends on the remaining service time $r$…

Probability · Mathematics 2017-10-05 Benjamin Legros , Ali Devin Sezer