Priority queueing model with balking and reneging

This investigation deals with two levels, single server preemptive priority queueing model with discouragement behaviour (balking and reneging) of customers. Arrivals to each level are assumed to follow a Poisson process and service times are exponentially distributed. The decision to balk / renege is made on the basis of queue length only. Two specific forms of balking behaviour are considered. The system under consideration is solved by using a finite difference equation approach for solving the governing balance equations of the queueing model, with infinite population of level 1 customer. The steady state probability distribution of the number of customers in the system is obtained

The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in Stochastic Model

Partially shared buffers with full or mixed priority

This paper studies a finite-sized discrete-time two-class priority queue. Packets of both classes arrive according to a two-class discrete batch Markovian arrival process (2-DBMAP), taking into account the correlated nature of arrivals in heterogeneous telecommunication networks. The model incorporates time and space priority to provide different types of service to each class. One of both classes receives absolute time priority in order to minimize its delay. Space priority is implemented by the partial buffer sharing acceptance policy and can be provided to the class receiving time priority or to the other class. This choice gives rise to two different queueing models and this paper analyses both these models in a unified manner. Furthermore, the buffer finiteness and the use of space priority raise some issues on the order of arrivals in a slot. This paper does not assume that all arrivals from one class enter the queue before those of the other class. Instead, a string representation for sequences of arriving packets and a probability measure on the set of such strings are introduced. This naturally gives rise to the notion of intra-slot space priority. Performance of these queueing systems is then determined using matrix-analytic techniques. The numerical examples explore the range of service differentiation covered by both models