Engineering Calculation of Overflow Probabilities in Buffers with Markov-Interrupted Service

Abstract

Interrupted service, which may occur in fading radio channels, in low-priority channels which can be preempted or in systems with failures may make severe demands on buffer size if overflow is to be avoided. This paper analyzes a buffer with a Markov-interrupted timeslotted server, generalizing earlier work on independent random interruptions. An equivalent service distribution is defined for use in an approximate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M/G/1</tex> model, which in turn gives buffer probabilities and overflow probabilities. For very small overflow probabilities, the necessary buffer size is found from a further analytic approximation to the tail of the buffer size distribution. The accuracy of the two approximations together is good, shown by an example of a fading radio channel.