95 research outputs found
An approximate analysis of a bernoulli alternating service model
We consider a discrete-time queueing system with one server
and two types of customers, say type-1 and type-2 customers. The server
serves customers of either type alternately according to a Bernoulli pro-
cess. The service times of the customers are deterministically equal to
1 time slot. For this queueing system, we derive a functional equation
for the joint probability generating function of the number of type-1 and
type-2 customers. The functional equation contains two unknown partial
generating functions which complicates the analysis. We investigate the
dominant singularity of these two unknown functions and propose an
approximation for the coefficients of the Maclaurin series expansion of
these functions. This approximation provides a fast method to compute
approximations of various performance measures of interest
Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations
In this paper, asymptotic properties of the loss probability are considered
for an M/G/1/N queue with server vacations and exhaustive service discipline,
denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss
probability are obtained for the cases in which the traffic intensity is
smaller than, equal to and greater than one, respectively. When the vacation
time is zero, the model considered degenerates to the standard M/G/1/N queue.
For this standard queueing model, our analysis provides new or extended
asymptotic results for the loss probability. In terms of the duality
relationship between the M/G/1/N and GI/M/1/N queues, we also provide
asymptotic properties for the standard GI/M/1/N model
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