Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary ...

We use the Method of Collective Marks to analyze some time-dependent processes in the M/G/1 queue with single and multiple vacations. With the server state specified at a fixed time t > 0, the Laplace transforms with respect to t of mixed transforms for the joint distribution of the number of departures by time t, the queue length, the virtual waiting time, the elapsed and remaining service/vac...

In this paper, we discuss a batch arrival bulk service queue with rework for the faculty item, possibility of breakdown, repair, and two kinds multiple vacation different threshold policy. The server serves remaining after repair completion. This type queuing model has lot applications in manufacturing/ production industries. Performance measures stability conditions are obtained. Numerical ill...

This paper gives a new method to derive the time average distribution of queue length in the model M/G/1 with many vacation rules. We extract many kinds of regenerative cycles of the well-known regenerative processes from the queue length process of the model by using the method shown by Fuhrmann and Cooper. The time average of the original model is represented by the combination of the time av...

Abstract In this paper, a new discrete-time GeomX /G/1 queue model with multiple vacations is analyzed. The Probability Generating Function (P.G.F.) of the queue length is obtained by using the method of an embedded Markov chain, and the mean of the queue length is obtained by using L’Hospital rule. Then the P.G.F. of the busy period is derived, and the probabilities for the system being in a b...

The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exp...

An M/M/1 queueing system with second optional service and unreliable server is studied. We consider that the server works at different rate rather than being idle during the vacation period. The customers arrive to the system according to Poisson process with state dependent rates depending upon the server’s status. All customers demand the first essential service whereas only some of them dema...