This paper considers a single-server retrial queue with constant retrial rate and batch arrivals, where an unreliable server may take an additional optional vacation after the first essential vacation. Customers arrive at the system according to a compound Poisson process, and they are served immediately if the server is available; otherwise, they will enter a retrial orbit and form a single wa...

We derive performance measures for burst arrival (e.g. messages of variable length packets) M / G / 1 queues with server vacations, controlled by the, so called, Randomly Timed Gated (RTG) protocol, operating as follows : Whenever the server returns from a ( general-type ) vacation and initiates a busy period, a Timer with random duration T is activated. If the server empties the queue before t...

This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system len...

A repairable 1 M G / / retrial queue with general retrial times, Bernoulli vacation, setup times and two-phase service is investigated in this paper. Customers are allowed to balk and renege at particular times. We assume that the customers who find the server busy or down are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. All customers demand the first “ess...

This paper mainly deals with a two phase service queueing model with gated service vacation. In this gated service vacation model, only those customers who are present in the queue when the server starts a batch mode service are taken into the batch. We have derived probability generating functions of the system size and the orbit size. We have investigated the conditions under which the steady...

In this paper we demonstrate that the distributional laws that relate the number of customers in the system (queue), L (<?) and the time a customer spends in the system (queue), S (W) under the first-in-first-out (FIFO) discipline lead to a complete solution for the distributions of L, Q, S, W for queueing systems which satisfy distributional laws for both L and Q {overtake free systems). Moreo...