The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down state otherwise the service of the customer at the head of the batch is started by the server. The service is provided in k</em...

Performance evaluation of transport layer protocols in cognitive radio sensor networks (CRSNs) is useful to provide quality-of-service for real-time reliable applications. This paper develops an analytical framework to model the steady-state sending rate of collecting cognitive radio (CR) sensors in rate-based generic additive-increase multiplicative-decrease (AIMD) and additive-increase additi...

We consider a class of two-queue polling systems with exhaustive service, where the order in which the server visits the queues is governed by a discrete-time Markov chain. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we obtain explicit expressions for the Laplace-Stieltjes trans...

Abstract In this paper, a new discrete-time GeomX /G/1 queue model with multiple vacations is analyzed. The Probability Generating Function (P.G.F.) of the queue length is obtained by using the method of an embedded Markov chain, and the mean of the queue length is obtained by using L’Hospital rule. Then the P.G.F. of the busy period is derived, and the probabilities for the system being in a b...

We consider a multiserver queuing process speciied by i.i.d. interarrival time, batch size and service time sequences. In the case that diierent servers have diierent service time distributions we say the system is heterogeneous. In this paper we establish conditions for the queuing process to be characterized as a geometrically Harris recurrent Markov chain, and we characterize the stationary ...

An important fundamental problem in green communications and networking is the operation of servers (routers or base stations) with sleeping mechanism to optimize energy-delay tradeoffs. This problem is very challenging when considering realistic bursty, non-Poisson traffic. We prove for the first time the optimal structure of such a sleep mechanism for multiple servers when the arrival of jobs...

Since an M D queue is represented by a Markov chain we can consider the set of all the M D queues as a subset of Markov chains A geometric structures is induced from the geometric structure of the set of Markov chains which forms an exponential family In this paper we show that in the large deviation of the tail probability of the queue length of an M D the rate function and a twisted Markov ch...

An efficient yet accurate estimation of the tail distribution of the queue length has been considered as one of the most important issues in call admission and congestion controls in ATM networks. The arrival process in ATM networks is essentially a superposition of sources which are typically bursty and periodic either due to their origin or their periodic slot occupation after traffic shaping...

In this paper we study a single-server queue where the inter-arrival times and the service times depend on a common discrete time Markov Chain. This model generalizes the well-known MAP/G/1 queue by allowing dependencies between interarrival and service times. The waiting time process is directly analyzed by solving Lindley’s equation by transform methods. The Laplace Stieltjes transforms (LST)...

This paper considers a repairable system with a repairman, who can take multiple vacations. If the system fails and the repairman is on vacation, it will wait for repair until the repairman is available. Assume that the system cannot be repaired ‘‘as good as new’’ after failures. Under these assumptions, using the geometric process and the supplementary variable technique, some important reliab...