Showing papers on "Retrial queue published in 2000"

Ergodicity of the BMAP/PH}/s/s+K retrial queue with PH-retrial times

Abstract: Define the traffic intensity as the ratio of the arrival rate to the service rate. This paper shows that the BMAP/PH}/s/s+K retrial queue with PH-retrial times is ergodic if and only if its traffic intensity is less than one. The result implies that the BMAP/PH}/s/s+K retrial queue with PH-retrial times and the corresponding BMAP/PH}/s queue have the same condition for ergodicity, a fact which has been believed for a long time without rigorous proof. This paper also shows that the same condition is necessary and sufficient for two modified retrial queueing systems to be ergodic. In addition, conditions for ergodicity of two BMAP/PH}/s/s+K retrial queues with PH-retrial times and impatient customers are obtained.

On the busy period of the M/G/1 retrial queue

Abstract: The M/G/1 queue with repeated attempts is considered. A customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers. Each customer in the pool repeats his demand after a random amount of time until he finds the server free. We focus on the busy period L of the M/G/1$ retrial queue. The structure of the busy period and its analysis in terms of Laplace transforms have been discussed by several authors. However, this solution has serious limitations in practice. For instance, we cannot compute the first moments of L by direct differentiation. This paper complements the existing work and provides a direct method of calculation for the second moment of L.

On The Single Server Retrial Queue With Balking

Abstract: We are concerned with the M/G/1 retrial queue with balking. The ergodicity condition is first investigated making use Of classical mean drift criteria. The limiting distribution of the number of customers in the system is determined with the help of a recursive approach based on the theory of regenerative processes. Many closed form expressions are obtained when we reduce to the M/M/1 queue for some representative balking policies.

An MX /G/1 retrial queue with exhaustive vacations

Abstract: We consider an MX /G/1 retrial queue with batch arrivals and server vacations, when the works for service and vacation tasks are arbitrary distributed. We obtain here the generating function of the number of customers in the system and in orbit in stationary regime. We also discuss stochastic decomposition property and the problem of the optimal control of the vacation policy.

Individual equilibrium dynamic routing in a multiple server retrial queue

Abstract: Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate l. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean m−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean n−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

Transient distributions of level dependent quasi-birth-death processes with linear transition rates

Abstract: Many queueing systems such asM/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers andMAP/M/∞ queue can be modeled by a level dependent quasi-birth-death (LDQBD) process with linear transition rates of the form λk = α+ βk at each levelk. The purpose of this paper is to propose an algorithm to find transient distributions for LDQBD processes with linear transition rates based on the adaptive uniformizaton technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results.