S. Pavai Madheswari

The M/G/1 retrial queue with feedback and starting failures

This paper discusses a retrial queue with Bernoulli feedback, where the server is subjected to starting failure. The retrial time is assumed to follow an arbitrary distribution and the customers in the orbit access the server under FCFS discipline. The necessary and sufficient condition for the stability of the system is derived. Various performance measures are obtained. Some numerical results are illustrated. The general decomposition law is shown to hold good for this model also. Some of the existing results are deduced as special cases.

Transient analysis of a single server queue with catastrophes, failures and repairs

Abstract A transient solution is obtained analytically using continued fractions for the system size in an M/M/1 queueing system with catastrophes, server failures and non-zero repair time. The steady state probability of the system size is present. Some key performance measures, namely, throughput, loss probability and response time for the system under consideration are investigated. Further, reliability and availability of the system are analysed. Finally, numerical illustrations are used to discuss the system performance measures.

An M/M/2 queueing system with heterogeneous servers and multiple vacations

In this paper, a Markovian queue with two heterogeneous servers and multiple vacations has been studied. For this system, the stationary queue length distribution and mean system size have been obtained by using matrix geometric method. The busy period analysis of the system and mean waiting time distribution are discussed. Extensive numerical illustrations are provided.

Transient Analysis of an M/M/1 Queue Subject to Catastrophes and Server Failures

ABSTRACT A transient solution for the system size in the M/M/1 queueing system with the possibility of catastrophes and server failures is analyzed. The steady state probabilities of the system size are also derived. Some important performance measures are discussed. Finally, the reliability and availability of the system are obtained.

Mx/G/1 Retrial Queue with Multiple Vacations and Starting Failures

This paper is concerned with the analysis of a single-server batch arrival retrial queue with Bernoulli service schedule and multiple vacation with general retrial times and the server being subjected to starting failures. We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served) discipline and only the customer at the head of the queue is allowed for access to the server. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution as well as some performance measures of the system under steady-state condition. We show that the general stochastic decomposition law for Mx/G/1 queue with multiple vacation models holds for the present system too. Some special cases are also studied.

An M/G/1 Bernoulli feedback retrial queueing system with negative customers

A single server retrial queue with negative customers and two types of Bernoulli feedback is considered. A necessary and sufficient condition for the system to be stable is investigated. The system size probabilities at output epochs are obtained by using an embedded Markov chain. Further, the joint generating functions of queue length and server status are studied by using supplementary variables method. Some important system performance measures are derived. Busy period of the system is also discussed. Finally, extensive numerical illustrations are provided.A single server retrial queue with negative customers and two types of Bernoulli feedback is considered. A necessary and sufficient condition for the system to be stable is investigated. The system size probabilities at output epochs are obtained by using an embedded Markov chain. Further, the joint generating functions of queue length and server status are studied by using supplementary variables method. Some important system performance measures are derived. Busy period of the system is also discussed. Finally, extensive numerical illustrations are provided.

Analysis of an M /M /N queue with Bernoulli service schedule

In this paper, a Markovian multiple server queue in which each server takes vacation according to Bernoulli scheduling service has been studied. For this system, the stationary queue length distribution and several performance characteristics are obtained using the matrix geometric solution technique. The system busy period and waiting time distribution have been discussed. The 1-limited service and exhaustive service with multiple vacations have been analysed as special cases. Extensive numerical illustrations are provided.

Transient and steady-state analysis of queueing systems with catastrophes and impatient customers

Sudhesh (2010) has discussed the transient probabilities for queueing systems subject to catastrophic failures and impatience of customers. However, it contains some errors concerning the terminology and the final forms of the transient probabilities of the system size. In this paper, we correct the errors and obtain the correct results in the work carried out by Sudhesh. In addition, the steady state system size probabilities and performance measures are provided. Finally, two special cases are deduced from the more general queueing model under study.

Queuing system with state-dependent controlled batch arrivals and server under maintenance

This paper deals with a single server Markovian queue subject to maintenance of the server. A batch of customers is allowed whenever the server is idle such that each individual customer in the batch is subject to a control admission policy upon arrival. Explicit expressions are obtained for the time dependent probabilities of the system size in terms of the modified Bessel functions. The steady state analysis and key performance measures of the system are also studied. Finally, some numerical illustrations are presented.