Accessible bibliography on retrial queues: Progress in 2000-2009

In this paper we survey work related to queues with interruptions that occur due to many reasons such as server breakdowns, servers taking emergency breaks, and customers having incomplete information or getting distracted We look at both continuous and discrete time queueing models with interruptions in this survey

Queues with interruptions: a survey

A batch arrival retrial queue with general retrial times under bernoulli vacation schedule for unreliable server and delaying repair

In this article, we present a feasibility analysis for performing vehicular dynamic spectrum access across vacant television channels via a queueing theory approach. In this study, we model the vacant TV channels as a multiserver, multipriority, preemptive queue. Queueing theory has been extensively employed in the open literature to model multiple access architectures as well as analyze network performance in both wired and wireless communication frameworks. On the other hand, to the best of the authors' knowledge, not many researchers have tried to resort to a queueing theory approach to analyze dynamic spectrum access networks on a system level, including the specific case of vehicular dynamic spectrum access (VDSA). Leveraging previously reported quantitative measurements obtained from a wireless spectrum measurement campaign conducted along a major interstate highway (I-90) located in Massachusetts, we modeled vacant TV channels as a multiserver queueing system in which available servers represent vacant TV channels. The servers become unavailable from the perspective of a vehicle in a time/location-varying fashion such that they represent spatially occupied TV channels. Both M/M/m and M/G/m models are employed to evaluate the probability that a vehicle finds all channels busy, as well as to derive the expected waiting times. We also consider cases where there are multiple priority classes of service requests such as a channel request by a first--responder vehicle.

Feasibility analysis of vehicular dynamic spectrum access via queueing theory model

SummaryThis paper deals with the stochastic decomposition property for retrial queues. This property is connected with similar results for vacation models. As applications, the moments of the number of customers in orbit and the rate of convergence under high retrial intensity can be obtained.

Stochastic decomposition for retrial queues

An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair

This paper deals with the steady-state behavior of an M^X/G/1 retrial queue with an additional second phase of optional service and service interruption where breakdowns occur randomly at any instant while the server is serving the customers. Further, the concept of delay time is also introduced in the model. This model generalizes both the classical M^X/G/1 retrial queue with service interruption as well as the M^X/G/1 queue with second optional service and service interruption. We carry out an extensive analysis of this model.

A batch arrival retrial queueing system with two phases of service and service interruption

An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism

We consider an M
 X
 /G/1 queueing system with two phases of heterogeneous service and Bernoulli vacation schedule which operate under a linear retrial policy. In addition, each individual customer is subject to a control admission policy upon the arrival. This model generalizes both the classical M/G/1 retrial queue with arrivals in batches and a two phase batch arrival queue with a single vacation under Bernoulli vacation schedule. We will carry out an extensive stationary analysis of the system, including existence of the stationary regime, embedded Markov chain, steady state distribution of the server state and number of customer in the retrial group, stochastic decomposition and calculation of the first moment.

Kandarpa Deka

Papers

An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair

A batch arrival retrial queueing system with two phases of service and service interruption

An MX/G/1 unreliable retrial queue with two phases of service and Bernoulli admission mechanism

A batch arrival retrial queue with two phases of service and Bernoulli vacation schedule