An Approximate Method for Calculating Delays for a Family of Cyclic-Type Queues
Shlomo Halfin · Bell System Technical Journal · 1975
A study of the marker-register dial-tone delay problem in No. 5 crossbar switching machines led to a special type of cyclic queuing model. In this paper, we present a method for calculating approximately the steady-state delays of an arriving customer. When applied to the marker-register problem, the model emphasizes the order in which markers are assigned to waiting calls and the fact that part of the markers' time is unproductive when an “all registers busy” condition occurs. Some numerical results are presented, which agree with the observed phenomenon that, for a constant marker load, the delays of Touch-Tone® calls are influenced by the load on the dial-pulse originating registers, and vice versa. The results are compared to those of a simulation of the same problem. The numerical results compare favorably in the range of loads that produce a dial-tone speed of between 0.05 and 0.15.