Markovian retrial queues with two way communication

Abstract

In this paper, we first consider single server retrial queues with two way communication.Ingoing calls arrive at the server according to a Poisson process.Service times of these calls follow an exponential distribution. If the server is idle, itstarts making an outgoing call in an exponentially distributed time. The duration ofoutgoing calls follows another exponential distribution. An ingoing arriving call that findsthe server being busy joins an orbit and retries to enter the server after someexponentially distributed time. For this model, we present an extensive study in whichwe derive explicit expressions for the joint stationary distribution of the number ofingoing calls in the orbit and the state of the server, the partial factorial moments as well as their generating functions.Furthermore, we obtain asymptotic formulae for the joint stationary distribution and the factorial moments.We then extend the study to multiserver retrial queues with two way communication for which a necessary and sufficient conditionfor the stability, an explicit formula for average number of ingoing calls in the servers anda level-dependent quasi-birth-and-death process are derived.