Multilevel Bulk Service Queues

Emil Bahary and Peter Kolesar
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Emil Bahary: Western Electric Company, Princeton, New Jersey
Peter Kolesar: Columbia University, New York, New York

Operations Research, 1972, vol. 20, issue 2, 406-420

Abstract: This paper uses the imbedded-Markov-chain method to study bulk service queuing systems in which the server chooses the capacity and service mechanism depending on the number of customers waiting in line at the start of the service. It derives conditions under which the systems studied are ergodic and obtains the stationary state probability generating functions. A bilevel hysteretic bulk service system is studied in detail using numerical methods. A concept of system “scale” is introduced that permits the calculation of operating characteristics of large systems from those of small systems. This property is important because the computations for large systems are much more difficult, if not impossible, to perform. The characteristics studied are the expectation and variance of the queue size, the proportion of time each service level is used, and the transition rate between service levels.

Date: 1972
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