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On Discretionary Priority Queueing
Author(s) -
AviItzhak B.,
Brosh I.,
Naor P.
Publication year - 1964
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19640440603
Subject(s) - priority inheritance , priority queue , interrupt , queueing theory , service (business) , computer science , poisson distribution , priority ceiling protocol , queue , constant (computer programming) , operations research , computer network , business , telecommunications , mathematics , quality of service , statistics , dynamic priority scheduling , transmission (telecommunications) , rate monotonic scheduling , programming language , marketing
A priority regime is envisaged for single queuing systems composed of two customer populations with Poisson arrivals which is intermediate between the two extreme doctrines: a) head of the line priority, b) pre‐emptive priority. The state of intermediacy is represented by discretionary powers vested in the server to interrupt recently initiated ‐ and not to interrupt almost completed ‐ service to a low priority customer upon the arrival of a high priority customer. For the case of constant service times the discretionary rule is defined and the ensuing queueing characteristics analyzed; in particular, the average total queue lengths of both high and low priority customers are derived for two different cases: a) the resume situation where service renewed to a low priority customer starts at the point of interruption; b) the repeat situation where service given to a low priority customer before an interruption, is completely lost. Optimisation procedures are outlined and for the resume situation a simple optimal discretionary rule is obtained.