Cyclic audit of a multichannel system

摘要

Many surveillance and quality-control systems consist of one auditor who cyclically audits multiple channels. An audit has infinitesimal duration unless the channel is occupied, in which case the audit ends on termination of the call. Initiation and duration of calls on a channel are independent of the auditor presence and of the occupancy of the other channels. On any channel, call duration is a random variable modeled by a gamma distribution, and the interarrival interval is an independent random variable from the same family. We provide formulae, dependent on the distribution of the time between audits of each channel, for statistics such as the expected time taken for the auditor to inspect all channels, the expected fraction of each call audited, and the expected percentage of calls audited. Complete solutions are obtained when the distribution of the interaudit time on a particular channel is approximated by a one-parameter family: gamma and delta families are modeled, as well as a realistic mixed distribution.