Showing papers on "Retrial queue published in 1993"

On the single server retrial queue with priority customers

Abstract: We consider anM2/G2/1 type queueing system which serves two types of calls. In the case of blocking the first type customers can be queued whereas the second type customers must leave the service area but return after some random period of time to try their luck again. This model is a natural generalization of the classicM2/G2/1 priority queue with the head-of-theline priority discipline and the classicM/G/1 retrial queue. We carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition, limit theorems under high and low rates of retrials and heavy traffic analysis.

The M/G/1 Retrial Queue With Retrial Rate Control Policy

Abstract: We consider a single-server retrial queueing system where retrial time is inversely proportional to the number of customers in the system. A necessary and sufficient condition for the stability of the system is found. We obtain the Laplace transform of virtual waiting time and busy period. The transient distribution of the number of customers in the system is also obtained.

An M/M/1 retrial queue with control policy and general retrial times

Abstract: We consider anM/M/1 retrial queueing system in which the retrial time has a general distribution and only the customer at the head of the queue is allowed to retry for service. We find a necessary and sufficient condition for ergodicity and, when this is satisfied, the generating function of the distribution of the number of customers in the queue and the Laplace transform of the waiting time distribution under steady-state conditions. The results agree with known results for special cases.

Monotonicity properties of single-server retrial queues

Abstract: A single server retrial queue is a queueing system consisting of a primary queue with finite capacity, an orbit and a server. Customers can arrive at the primary queue either from outside the system or from the orbit. If the primary queue is full, an arriving customer joins the orbit and conducts a retrial later. Otherwise, he enters the primary queue, waits for service and then leaves the system after service completion. We investigate the effect of retrial times on the behavior of the system. In particular, we assume that the retrial time distributions are phase type and introduce a new relation, which we call K-dominance (short for Kalmykov), on these distributions. Longer retrial times with respect to this K-dominance are shown to result in a more congested system in the stochastic sense. From these results, we derive monotonicity properties of several system performance measures of interest.

Stability condition for a single-server retrial queue

Abstract: A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system. We investigate the stability condition for a single-server retrial queue. Let A be the arrival rate and 1/p be the mean service time. It has been proved that A/p <1 is a sufficient stability condition for the M/G/1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that A/M < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

Explicit Formulae for the Characteristics of the M/H2/1 Retrial Queue

Abstract: In this paper we study the M/H2/1 queue with returning customers. We obtain explicit formulae for the steady-state distribution and the expected quality characteristics of the system. In addition, a simple recursion scheme for computing the 'orbit' busy period is proposed.

On the virtual waiting time for an M/G/1 retrial queue with two types of calls

Abstract: We consider an M/G/1 retrial queueing system with two types of calls which models a telephone switching system. In the case that arriving calls are blocked due to the channel being busy, the outgoing calls are queued in priority group whereas the incoming calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the Laplace-Stieltjes transform of the distribution of the virtual waiting time for an incoming call. When the arrival rate of outgoing calls is zero, it is shown that our result is consistent with the known result for a retrial queueing system with one type of call.

Maximum Entropy Analysis of Queueing Network Models

Abstract: The principle of Maximum Entropy (ME) provides a consistent method of inference for estimating the form of an unknown discrete-state probability distribution, based on information expressed in terms of true expected values. In this tutorial paper entropy maximisation is used to characterise product-form approximations and resolution algorithms for arbitrary continuous-time and discrete-time Queueing Network Models (QNMs) at equilibrium under Repetitive-Service (RS) blocking and Arrivals First (AF) or Departures First (DF) buffer management policies. An ME application to the performance modelling of a shared-buffer Asynchronous Transfer Mode (ATM) switch architecture is also presented. The ME solutions are implemented subject to Generalised Exponential (GE) and Generalised Geometric (GGeo) queueing theoretic mean value constraints, as appropriate. In this context, single server GE and GGeo type queues in conjunction with associated effective flow streams (departure, splitting, merging) are used as building blocks in the solution process. Physical interpretations of the results are given and extensions to the quantitative analysis of more complex queueing networks are discussed.