Research & Reviews: Journal of Statistics Special Issue on Recent Statistical Methodologies and Applications (Vol.2) e-ISSN: 2278-2273, p-ISSN: 2348-7909 RRJS (2014) 94-98 © STM Journals (2014). All Rights Reserved Page 94 Parameter Estimation of Single Server Queue with Working Vacations K.Senthamarai Kannan 1 and A. Jabarali 2 * 1 Professor, 2 Research Scholar, Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu - 627 012, India Abstract Queue is a waiting line phenomenon. The server may take the vacation due to breakdown or other reasons. If the server is on vacation, there is a situation the customers have to wait for service during that period. The generalization of the classical vacation model is considered as the server which gives the service at different rate rather than completely stopping the service during the vacation period. This paper deals with the estimation of the parameters in M/M/1 queue during working vacations period. The maximum likelihood estimation procedure is applied to obtain the estimation of the model parameters and also the performance measure of queueing system had been discussed. Finally computational results are presented for the queueing model. Keywords: M/M/1 queue, vacation model, working vacations, maximum likelihood estimation, performance measures. *Author for Correspondence E-mail: statjafar@gmail.com INTRODUCTION Statistical inference in queueing theory has drawn the attention of researchers in the past few decades. The problem of estimation concerning the parameters of queueing process such as arrival rate, service rate and traffic intensity is the most important thing in the queueing systems [1, 2]. The pioneer investigators have derived the Maximum Likelihood Estimates(MLE) for the arrival and service parameters of an M/M/1 queueing model [3] and infinite server queueing model [4]. Examining the MLE and Moment Estimate(ME) of the parameters of the inter- arrival and service time distributions of GI/G/1 queue model are discussed in Ref. [5]. Consequently, the inferential procedures concerning the traffic intensity of M/E K /1 queue model are discussed in Ref. [6]. The stationary solution of MLE of Markovian two server queueing model parameters have been obtained in the case of non-identical servers [7]. Later, stationary solution of MLE of the generalized form of multi-server queueing model in the presence of non-identical servers and the Confidence Intervals(CI) of these model parameters are obtained [8]. Meanwhile, the MLE and Bayesian estimates of the M/M/1/1 queueing model parameters are explained and discussed the large sample test for the model parameters [9]. Over the last two decades, the queueing systems with vacations have been well studied because of their applications in modeling the computer networks, communication and manufacturing/ service systems. In the previous studies of classical vacation queueing models, it is assumed that the server stops the primary service completely and utilizes the vacation time for other secondary jobs. The working vacations in M/M/1 queueing model was introduced in Ref. [10], the concept of working vacation in M/M/1 queue, where the server works at a lower rate rather than completely stopping the primary service during the vacation period. They have considered multiple vacation policy and derived the simple explicit formula for the mean, variance, the probability generating function of number of customers in the system, the Laplace-Stieltjes Transform(LST) of waiting time distribution and the applications of these queueing model is connected to performance analysis of gateway router in communication networks. Recently, working vacation in M/M/1 queueing model was considered in Ref. [11], they have obtained the stationary distribution of the