Related papers: Explicit Results for the Distributions of Queue Le…
We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level…
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…
Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: the retrial queueing systems with priority. This type of queueing system is…
Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…
We consider $M/G/\infty$ queues with gated service and obtain results on the distribution of the stage length and the number of customers served in a stage when the system is stationary. The stage length density is expressed as an infinite…
Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is…
Traffic state estimation plays an important role in facilitating effective traffic management. This study develops a combinatorial approach for nonparametric short-term queue length estimation in terms of cycle-by-cycle partially observed…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally…
We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
We introduce a fractional generalization of the Erlang Queues $M/E_k/1$. Such process is obtained through a time-change via inverse stable subordinator of the classical queue process. We first exploit the (fractional) Kolmogorov forward…
We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…
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…
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
This paper studies the queue length process in series Jackson networks with external input to the first station. We show that its Markov transition probabilities can be written as a finite sum of non-crossing probabilities, so that…
A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…
As a follow-up to a recent paper considering two symmetric queues, the \textit{Shortest Queue First} service discipline is presently analysed for two general asymmetric queues. Using the results previously established and assuming…
After a short report of results on infinite servers queues systems, focusing on its busy period, using networks of queues with infinite servers nodes a model is constructed to study a two echelons repair system. These repair systems may be…