Search

The present study considers a single-server Markovian queueing system by observing the number of customer arrivals during the service time of a customer. We estimate the traffic intensity in this queueing system along with the average queue length and the expected number of customers in the system. We propose classical and Bayesian frameworks to estimate the parameters of interest. In the Bayesian setup, three forms of prior distributions for ρ and two loss functions are considered. Furthermore, the predictive distribution of the number of customer arrivals during the service time of a customer and the equal-tailed credible region of ρ are obtained. The aforementioned approaches are illustrated with numerical examples based on simulation studies. [ABSTRACT FROM AUTHOR]

This paper considers an infinite buffer renewal input queue with multiple working vacation policy wherein customers are served by a single server according to general bulk service (a, b)-rule (1 ≤ a ≤ b). If the number of waiting customers in the system at a service completion epoch (during a normal busy period) is lower than ‘a’, then the server starts a vacation. During a vacation if the number of waiting customers reaches the minimum threshold size ‘a’, then the server starts serving this batch with a lower rate than that of the normal busy period. After completion of a batch service during working vacation, if the server finds less than ‘a’ customers accumulated in the system, then the server takes another vacation, otherwise the server continues to serve the available batch with that lower rate. The maximum allowed size of a batch in service is ‘b’. The authors derive both queue-length and system-length distributions at pre-arrival epoch using both embedded Markov chain approach and the roots method. The arbitrary epoch probabilities are obtained using the classical argument based on renewal theory. Several performance measures like average queue and system-length, mean waiting-time, cost and profit optimization are studied and numerically computed. [ABSTRACT FROM AUTHOR]

We consider a single server renewal input queueing system under multiple vacation policy. When the system becomes empty, the server commences a vacation of random length, and either begins an ordinary vacation with probability q (0 ≤ q ≤ 1) or takes a working vacation with probability 1 - q. During a working vacation period, customers can be served at a rate lower than the service rate during a normal busy period. If there are cus- tomers in the system at a service completion instant, the working vacation can be interrupted and the server will come back to a normal busy period with probability p (0 ≤ q ≤ 1) or continue the working vacation with probability 1 - p. The server leaves for repeated vacations as soon as the system becomes empty. Upon arrival, customers decide for themselves whether to join or to balk, based on the observation of the system-length and/or state of the server. The equilibrium threshold balking strategies of customers under four cases: fully observable, almost observable, almost unobservable and fully unobservable have been studied using embedded Markov chain approach and linear reward-cost structure. The probability distribution of the system-length at pre-arrival epoch is derived using the roots method and then the system-length at an arbitrary epoch is derived with the help of the Markov renewal theory and semi-Markov processes. Various performance measures such as mean system-length, sojourn times, net benefit are derived. Finally, we present several numerical results to demonstrate the effect of the system parameters on the performance measures. [ABSTRACT FROM AUTHOR]