The bottleneck in many telecommunication systems has often been modeled by an M/G/1 queueing system with priorities. While the probability generating function for the occupancy distribution of each traffic classes can be readily obtained, the occupancy distributions have been obtainable only rarely. However, the occupancy distribution is of great importance, particularly in those cases where th...

Abstract: In this paper, we present a performance analysis of a system with two multiplexers in tandem. Each multiplexer is fed by an external arrival process that consists of the superposition of the traffic generated by independent binary Markov sources. Further, the output of the first multiplexer is fed into the second multiplexer according to an independent Bernoulli process. The probabili...

In this paper, we present an exact transient (discrete-time) queuing analysis of a statistical multiplexer with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets. The functional equation describing this queuing model is manipulated and transformed into a mathematical tractable form. This allows us to derive t...

This paper studies the / / 1 Geo G queue model with , p N policy set-up time, multiple vacation and disasters. The server will start up the random set-up period with the probability p if the customer number is at least N at the end of a random length V of the holiday. Otherwise, the server takes vacation repeatedly with the probability p . Using embedded Markov chain and supplemental variable m...

The Asymmetric Simple Inclusion Process (ASIP) is an n-site tandem stochastic network with a Poisson arrival influx into the first site. Each site has unlimited buffer gate in front of it. opens, independently all other gates, following site-dependent Exponential inter-opening time. When site’s particles occupying move simultaneously to next In this paper, Generalized ASIP analyzed where sites,...

n X n Y                  of 0 0 1 1 , , , 0 1 0 1 S                                    valued Markov dependent bivariate trials. By using the method of conditional probability generating functions (pgfs), we derive the pgf of joint distribution of   1 1 2 2 0 1 0 1 0 1 0 1 , , , , , ; , n k n k n k n k X X Y Y where for , de0,1 i  1 , i i n...

We present a mathematical formulation to evaluate the effects of gestational mutations on cancer risk. The hazard or incidence function of cancer is expressed in terms of the Probability Generating Function (PGF) of the number of normal and mutated cells at birth. Using Filtered Poisson Process Theory, we obtain the PGF for several models for the accumulation of gestational mutations. In partic...

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...

In this paper, we analyze a bulk input Geom/Geom/1 queue with single working vacation. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived, from which we got the stochastic decomposition result for the PGF of the stationary queue size. It is important that we find the biparameter addition theorems of the conditional negative binomial distribu...

We study the single server queueing system with two types of Abstract failure to servicechannels including the preemptive priority to the repair of major failure. The units arrive at thesystem in a poisson fashion and are served exponenitally. The steady - state probabilities ofvarious states by using generating function have been obtained.