Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate

Diffusion Approximations for G/M/n + GI Queues with State-Dependent Service Rates

We consider a sequence of many-server queueing systems with impatient customers of the type G/M/n+GI in heavy traffic. This sequence is indexed by n, where the parameter n represents the number of servers in the nth system. The state process is considered to be the diffusion-scaled total customer count in the system and the service rate is a state-dependent perturbation of a given basic service...

An efficient method to compute the rate matrix for retrial queues with large number of servers

The approximate solution technique for the main M/M/c retrial queue based on the homogenization of the model employs a quasi-birth-death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the matrixgeometric method, which involves the computation of the rate matrix R. This paper is motivated...

Single retrial queues with service option on arrival

Stability of Retrial Queues with Versatile Retrial Policy

We consider in this paper the stability of retrial queues with a versatile retrial policy. We obtain sufficient conditions for the stability by the strong coupling convergence to a stationary ergodic regime for various models of retrial queues including a model with two types of customers, a model with breakdowns of the server, a model with negative customers, and a model with batch arrivals. F...

Asymptotic Analysis for Markovian Retrial Queues with Two Types of Nonpersistent Customers

We consider Markovian multiserver retrial queues where a blocked customer has two opportunities for abandonment: at the moment of blocking or at the departure epoch from the orbit. In this queueing system, the number of customers in the system (servers and buffer) and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose stationary distribution is expressed in terms...