In this paper we carry out both light-traffic and heavy-traffic analyses for the calculation of steady-state loss probabilities in the general multi-server queuing loss system, the GI/G/n/0 queue. The analysis makes use of a heuristic approach called the GM Heuristic, for which a detailed analysis in normal traffic has previously been published. Sufficient conditions are given for the GM Heuristic to be asymptotically exact in light traffic. The heuristic is also shown to be asymptotically exact in heavy-traffic when the number of servers n tends to infinity. These results are illustrated numerically using two-phase Coxian distributions for both the inter-arrival time and service time.

In this paper, we introduce a new heuristic approach for the numerical analysis of queueing systems. In particular, we study the general, multi-server queueing loss system, the GI / G / n /0 queue, with an emphasis on the calculation of steady-state loss probabilities. Two new heuristics are developed, called the GM Heuristic and the MG Heuristic , both of which make use of an exact analysis of the corresponding single-server GI / G /1/0 queue. The GM Heuristic also uses an exact analysis of the GI / M / n /0 queue, while the MG Heuristic uses an exact analysis of the M / G / n /0 queue. Experimental results are based on the use of two-phase Coxian distributions for both the inter-arrival time and the service time; these include an error analysis for each heuristic and the derivation of experimental probability bounds for the loss probability. For the class of problems studied, it is concluded that there are likely to be many situations where the accuracy of the GM Heuristic is adequate for practical purposes. Methods are also developed for combining the GM and MG Heuristics. In some cases, this leads to approximations that are significantly more accurate than those obtained by the individual heuristics.

This paper is concerned with the solution of a specific hypercube queueing model. It extends the work that was described in a related paper by Atkinson et al. [Atkinson, J.B., Kovalenko, I.N., Kuznetsov, N., Mykhalevych, K.V., 2006. Heuristic methods for the analysis of a queuing system describing emergency medical services deployed along a highway. Cybernetics & Systems Analysis, 42, 379–391], which investigated a model for deploying emergency services along a highway. The model is based on the servicing of customer demands that arise in a number of distinct geographical zones, or atoms. Service is provided by servers that are positioned at a number of bases, each having a fixed geographical location along the highway. At each base a single server is available. Demands arising in any atom have a first-preference base and a second-preference base. If the first-preference base is busy, service is provided by the second-preference base; and, if both bases are busy, the demand is lost. In practice, because of differences in travel times from the first and second-preference bases to the atom in question, the service rate may be significantly different in the two cases. The model studied here allows for such customer-dependent service rates to occur, and the corresponding hypercube model has 3n states, where n is the number of bases. The computational intractability of this model means that exact solutions for the long-run proportion of lost demands (ploss) can be obtained only for small values of n. In this paper, we propose two heuristic methods and a simulation approach for approximating ploss. The heuristics are shown to produce very accurate estimates of ploss.

Consideration is given to a queueing model that describes the deployment of emergency medical service along a highway. Two heuristic methods are proposed for the approximate evaluation of stationary loss probability and utilization of ambulance cars. The high accuracy of these methods is demonstrated by several examples.

De Boer, van Dijkhuizen and Telgen (BDT) proposed the economic tender quantity (ETQ) model for determining how many suppliers should be invited to tender for the provision of certain types of product or service. They presented two general conclusions concerning the relationship between the optimal number of suppliers and the uncertainty in the bid price. We show, through counter-examples, that the BDT conclusions do not hold in general for all possible distributions of bid price. However, their first, and principal, conclusion does hold in those cases in which any change in the distribution of the bid price is equivalent to a positive linear transformation of the bid price. In addition, if this condition holds and an optimal policy is followed, we show that the ETQ value is an increasing function, and the expected total cost of tendering is a decreasing function, of the variance of the bid price. The degree to which the BDT conclusions can be said to be counter-intuitive for management decision-making, and the implications of the research presented in this paper, are also discussed.

A GI / G / m /0 loss system is considered. Three cases of light-traffic insensitivity of the loss probability to the shape of the service time distribution, given its first moment, are investigated in a triangle array setting.