This paper analyzes anM/M/2 queueing systemwith two heterogeneous servers, one of which is always available but the other goes on vacation in the absence of customers waiting for service. The vacationing server, however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady state using matrix geometric method. Busy period of the system is...

In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in M/G/1 vacation models operating under the N-, T and D-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biase...

We consider two models of M=G=1 and G=M=1 type queueing systems with restricted accessibility. Let (V (t))t¿0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let n be his arrival time. In both models there is a capacity bound v∗ ∈ (0;∞): In Model I the amount of service given to the nth customer is equal to min[Sn; v∗ − V ( n−)], i.e. ...

We obtain sufficient conditions for the finiteness of the moments of the single-server queue busy period in discrete and continuous time. In the cases of power and exponential moments, the conditions found coincide with the known necessary ones. 1. Introduction and notation. Consider a sequence t n n of random vectors with nonnegative coordinates which are i.i.d. in n, but any dependence betwee...

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In...

We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order...