We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoul...

This paper concentrates on the steady state analysis of the discrete-time batch arrival Geo/G/1 queue with vacations. In this model, after serving all customers in the system, the server will take a random maximum number of vacations before returning to the service mode. The distributions of busy period, vacation period and vacation cycle have been given. Meanwhile, the PGFs for the off-line pe...

This paper studies the operating characteristics of an MX/Hk/1 queueing system under multiple vacation policy. It is assumed that the server goes for vacation as soon as the system becomes empty. When he returns from a vacation and there is one or more customers waiting in the queue, he serves these customers until the system becomes empty again, otherwise goes for another vacation. The brea...

Consider a GI/Geo/1 queue with start-up period and single working vacation. When the system is in a closed state, an arriving customer leads to a start-up period. After the start-up period, the system becomes a normal service state. During the working vacation period, if there are customers at a service completion instant, the vacation can be interrupted and the server will come back to the nor...

In this paper, a bulk arrival general bulk service queueing model delayed service with restricted vacation policy, variant arrival rate and setup time is considered. The server starts the service only if at least ‘a’ customers are waiting in the queue, and renders the service according to the general bulk service rule with minimum of ‘a’ customers and maximum of ‘b’ customers, then the server w...

In this paper, we consider a discrete-time single-server finite-buffer batch arrival queue in which customers are served in batches according to a general bulk-service rule, that is, at least ‘a’ customers are needed to start a service with a maximum serving capacity of ‘b’ customers. The server takes a (single and multiple) vacation as soon as the queue length falls below ‘a’ at the completion...

In this paper the information theoretic principle of Maximum Entropy (ME) is applied, as a method of inference, towards the study of the M/G/1 queueing model at equilibrium with either single or multiple server vacation periods under both exhaustive and non-exhaustive scheduling schemes. An analytic ME approximation for the characterisation of a universal form for the queue length distribution ...

Abstract We consider an M/G/1 feedback queue with optional server vacations based on Bernoulli schedule and a single vacation policy. We assume that the server provides two types of service, type 1 with probability p1 and type 2 with probability p2 with the service times following general distribution and each arriving customer may choose either type of service. However after the completion of ...

In this paper a M /G(a,b)/|1 queuing system with multiple vacations, delayed service and setup time is considered. If the queue size is < ‘a’ after a service completion or after a vacation termination, the server goes for multiple vacation. Also after serving M batches continuously even if sufficient number of customers are there in the queue, the server goes for a vacation with probability α j...

This paper studies a batch arrival single server Bernoulli feedback queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and multiple vacations with exponential distributed with Mean vacation time . After first-stage service the server must provide the second stage service. However after the completio...