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A tandem queue with coupled processors: Computational issues. (English) Zbl 1094.60065
The paper considers a two-stage queue, where jobs arrive at the first station according to a Poisson process. After receiving service at this station, they move to the second station, and upon completion of service at the second station they leave the system. The amount of work that a job requires at each of the station is an exponentially distributed random variable, and the total service capacity of the two stations together is constant. When both stations are nonempty, a given proportion of the capacity is allocated to station 1, and the remaining proportion is allocated to station 2. If one of the stations is empty, however, the total service capacity of the stations is allocated to the nonempty station. The paper investigates the two-dimensional Markov process representing the numbers of jobs at the two stations. It is known that the problem of finding the bivariate generating function of the stationary distribution can be reduced to a Riemann-Hilbert boundary value problem. In general, obtaining performance measures from the formal solution of a Riemann-Hilbert boundary value problem is not straightforward. The paper discusses the computational issues that arise when obtaining performance measures.

60K25 Queueing theory (aspects of probability theory)
30E25 Boundary value problems in the complex plane
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
Full Text: DOI
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