Dealing with uncertainties in queues and networks of queues: A Bayesian approach.

*(English)*Zbl 0946.62025
Ghosh, Subir (ed.), Multivariate analysis, design of experiments, and survey sampling. A tribute to Jagdish N. Srivastava. New York, NY: Marcel Dekker. Stat., Textb. Monogr. 159, 579-608 (1999).

From the introduction: Queues are, unfortunatey for us, much too familiar to need detailed definitions. In a queueing system, customers arrive at some facility requiring some type of service; if the server is busy, the customer waits in line to be served. The familiar notion of a queue thus parallels its mathematical meaning. “Customer” and “server” do not necessarily mean people, but refer to very general entities.

This paper (mostly based on previous work of the authors) will highlight the advantages of Bayesian analyses of queues, pointing out also some of its shortcomings. It is basically a review of previous results, and thus mathematical details are kept to a minimum. Throughout this paper, results are demonstrated in simple examples using noninformative priors. The use of such priors allows for easy comparison with non-Bayesian results. Also, Bayesian answers with noninformative priors might be more appealing to non-die-hard Bayesians, since the controversial inclusion of influential prior information is avoided. (The interested reader can find details about informative analyses in the references mentioned in the paper.)

The paper contains seven sections, this Introduction being Section 1. In Section 2 we present the basic queueing models that we shall use in the rest of the paper. Sections 3 and 4 are devoted to a somewhat peculiar review of previous results developed through the study of some advantages (Section 3) and some difficulties (Section 4) of Bayesian analyses of queues. Section 5 introduces the very important area of queueing networks. Finally, in Section 6, we give a very succinct account of (Bayesian) inferences for queueing networks.

For the entire collection see [Zbl 0927.00053].

This paper (mostly based on previous work of the authors) will highlight the advantages of Bayesian analyses of queues, pointing out also some of its shortcomings. It is basically a review of previous results, and thus mathematical details are kept to a minimum. Throughout this paper, results are demonstrated in simple examples using noninformative priors. The use of such priors allows for easy comparison with non-Bayesian results. Also, Bayesian answers with noninformative priors might be more appealing to non-die-hard Bayesians, since the controversial inclusion of influential prior information is avoided. (The interested reader can find details about informative analyses in the references mentioned in the paper.)

The paper contains seven sections, this Introduction being Section 1. In Section 2 we present the basic queueing models that we shall use in the rest of the paper. Sections 3 and 4 are devoted to a somewhat peculiar review of previous results developed through the study of some advantages (Section 3) and some difficulties (Section 4) of Bayesian analyses of queues. Section 5 introduces the very important area of queueing networks. Finally, in Section 6, we give a very succinct account of (Bayesian) inferences for queueing networks.

For the entire collection see [Zbl 0927.00053].

##### MSC:

62F15 | Bayesian inference |

62M99 | Inference from stochastic processes |

60K25 | Queueing theory (aspects of probability theory) |