We study a system of two non-identical and separate M/M/1/• queues with capacities (buffers) C1 < ∞ and C2 = ∞, respectively, served by a single server that alternates between the queues. The server’s switching policy is threshold-based, and, in contrast to other threshold models, is determined by the state of the queue that is not being served. That is, when neither queue is empty while the se...

There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where 0< λ < 1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate...

In the author’s recent paper [11], it is established that in a multiclass single-server queue with regular service disciplines, the stationary distributions and their moments for workload as well as for queue length can be approximated by appropriate exponential distributions and their moments in the heavy-traffic regime. In this work, relaxing the assumption of moment generating function on th...

In this paper we consider a single-server cyclic polling system. Between visits to successive queues, the server is delayed by a random switch-over time. The order in which customers are served in each queue is determined by a priority level that is assigned to each customer at his arrival. For this situation the following service disciplines are considered: gated, exhaustive, and globally gate...

In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and low priority customers. For this situation the following service disciplines are considered: gated, globally gated, and exhaustive. We study the cycle time dis...

This paper presents an analysis of a cyclic-service tandem queue (M/C/l type queue) with exhaustive services and multiple server vacations, in which a single server takes repeated vacations until it finds at least one message in the first queue after emptying the queueing system. It is assumed that the vacation time is generally distributed, and switch-over times are zero. This paper analyzes q...

We consider a finite-buffer single-server queue with Markovian arrival process (MAP) where the server serves a limited number of customers, and when the limit is reached it goes on vacation. Both singleand multiple-vacation policies are analyzed and the queue length distributions at various epochs, such as pre-arrival, arbitrary, departure, have been obtained. The effect of certain model parame...

There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where 0 < λ < 1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate...