Abstract: We study the Nash equilibrium behavior of customers in a discrete-time single-server queue under multiple vacation policy or single vacation policy. Every arriving customer either joins the queue or balks based on his or her service utility. Using a Quasi-Birth-Death Processes (QBD) model, we obtain the stationary distribution of the queue length via the Matrix-Geometric Solution meth...

This paper investigates an M [x] /G/1 queueing system with an unreliable server, where the server may take an additional vacation after the essential vacation. If the system becomes empty, the server leaves the system and takes the essential vacation. At the end of the essential vacation, the server may return to the system with probability p or take another vacation with probability 1-p. When ...

We consider a problem of optimal production control of a single unreliable machine. The objective is to minimize a discounted convex inventory/backlog cost over an infinite horizon. Using the variational analysis methodology, we develop the necessary conditions of optimality in terms of the co-state dynamics. We show that an inventorythreshold control policy is optimal when the work and repair ...

In most queueing systems the server may be subjected to lengthy and unpredictable breakdowns while serving a customer. For instance, in manufacturing systems the machine may breakdown due to malfunction or job related problems; in computer systems, the machine may be subject to scheduled backups and predicted failures. In these systems, server breakdown results in a period of server unavailabil...

ON OPTIMAL POLICIES FOR MULTI·REPAIR·TYPE MARKOV MAINTENANCE MODELS Yukio Hatoyama Tokyo Institute of Technology (Received April 6, 1978) This paper treats an extension of an optimal machine maintenance model with Markovian deterioration introduced by Derman. The system consists of an operating machine whose deterioration is Markovian, a finite number of identical spare machines, and several ty...

This paper investigates a discrete-time impatient customer queue with Bernoullischedule vacation interruption. The vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steady-state probabilities at arbitrary and outside observer’s observation epochs using recursive technique. Cost analysis ...

An M/G/1 retrial queue subject to disasters and N-policy vacation is investigated in this paper. Both positive and negative customers arrival in Poisson processes independently, and positive customers receive service immediately if the server is idle upon their arrivals. Otherwise, they enter a retrial orbit and repeat their attempt again after a random time period. Once negative customers arri...

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...

We study a finite buffer N-policy GI/M(n)/1 queue with Bernoulli-schedule vacation interruption. The server works with a slower rate during vacation period. At a service completion epoch during working vacation, if there are at least N customers present in the queue, the server interrupts vacation and otherwise continues the vacation. Using the supplementary variable technique and recursive met...