By Alec M. Lee M.A. (auth.)
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This is all the discussion which we shall have of non-preemptive priorities in this book. The reader who wishes to pursue the matter further is advised to consult the works listed in the selected bibliography at the end of this book. The succinct account in the book by Cox and Smith is particularly recommended. PREEMPTIVE PRIORITIES If the reader will permit, this section must begin with a personal commentary. I have never encountered a situation where preemptive priority rules were in force, or where it was possible to enforce them even if it had been desirable, outside the fields of electronics and communications.
For this reason alone, the present discussion will be kept to a minimum. 42 APPLIED QUEUEING THEORY NON-PREEMPTIVE PRIORITIES Suppose that there are two classes of customers, C1 and C2 • Of all the customers entering the queueing-system for service, a belong to C1 and (I - a) to C2 . It is only necessary to consider two priority classes, as it is very simple to generalize the results for the two-class priority case to multiple-class priorities. When a customer of C1 arrives, he takes priority over any members of C2 who may be present, but behind any other members of C1 who may already be in the system.
Until very recent times but few attempts had been made to do so. Classical multiple-channel models mainly assumed the operation of a FIFO rule, and rarely of LIFO or SIRO rules. In any event they were based on the principle that all arriving customers would join a single queue, and that this queue would feed all service-channels with customers being drawn from it according to some clearly defined rule of the FIFO, LIFO or SIRO type. The possibility of disintegration-that is that the single queue would break down into several queues, perhaps one for each service-channel -and the associated phenomena of jockeying, preferential queueing and so on was not contemplated.