Nondeterministic Polling Systems

• Published in: Management science 1991-06, Vol.37 (6), p.667-681
• Main Author: Srinivasan, Mandyam M
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer systems; Conservation Laws; Determinism; Exact sciences and technology; Gas stations; Management science; Mathematical expressions; Mathematical models; Mathematical moments; mean waiting times; Network servers; Operational research and scientific management; Operational research. Management science; polling systems; Polls; queueing theory; Queuing theory. Traffic theory; Random variables; Service stations; Studies; Vehicles
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.37.6.667

A nondeterministic polling system is considered in which a single server serves a number of stations. The service discipline at each station is, consistently, either nonexhaustive, semiexhaustive, gated, or exhaustive. If the server polls a station i which uses either the nonexhaustive or the semiexhaustive service discipline, then the next station polled is station j with probability p ij if there was service at station i . The service time at station i is a random variable which may depend on the station polled next. If no service is performed at station i , then the next station polled is station j with probability e ij . The time to switch between stations i and j is a random variable which may depend on whether service was performed at station i or not. If the server polls a station i that follows either the exhaustive service discipline or the gated service discipline, then the next station polled is station j with probability p ij regardless of whether there was service at station i or not. Cycle times and stability conditions are derived for this system, and Conservation Laws are obtained which express a weighted sum of the mean waiting times in terms of known data parameters. For systems with a mix of exhaustive and gated service stations, we show how the individual mean waiting times can be obtained.