8.1.2 What-Design a Non-perfectly Working System?

A few years ago one of us was involved in a very short term (one person month of total effort) study for scheduling telephone operators in a new city-wide 911 system for New York City. The three-digit number 911 is now being implemented throughout the United States as a standardized emergency public safety number through which callers are linked to the local police or fire department or ambulance service. However, at the time of this study, it was a relatively novel concept. In New York's 911 installation, queueing delays had become intolerable during certain periods of the day and days of the week. Simple M/M/N queueing theory provided a reasonable initial procedure for rescheduling the personnel to reduce significantly the delays experienced. ² However, to perform the rescheduling, it was necessary to have the police commissioner (or his designated representative) state an allocation objective of the following type:

Specify desired values for T and P, so that no more than P percent of the 911 calls will be delayed T or more seconds.

For instance, if T = 15 and P = 5, then the rescheduling based on the M/M/N queue would allocate a sufficient number of telephone operators N(t) during hour t so that no more than 5 percent of the calls would be delayed 15 or more seconds. While an average of 17 percent of calls were being delayed 15 or more seconds in the existing system, there were predictable periods during which 40 percent of the calls were being delayed 30 or more seconds. However, the police commissioner was quite reluctant to provide values for T and P. Finally, he settled on T = P = 0.0. But, given the probabilistic nature of queueing systems, such perfect operation is virtually impossible with a finite number of servers.

The commissioner's unwillingness to specify a positive value for P clearly rested in his uneasiness in acknowledging (and approving!) a system that functions imperfectly. Imagine a headline in a local newspaper, if the information were leaked that T = 15 seconds and P = 5 (assuming that 10,000 calls are received per day): "Police Commissioner Approves Excessive Delay in Answering 182,500 Police Calls This Year!"

Therefore, not only are explicit statements of objectives difficult to elicit, but they are even more difficult when they contain a certain admission of failure as a result of the probabilistic nature of the system.

This case has both a happy and a sad ending. Back at the drawing board, it was decided to redefine the problem as that of rescheduling the currently available person-hours to achieve the lowest possible mean queueing delay throughout all hours of the day. Thus, the problem became one of redeploying person-hours during relatively overstaffed periods to understaffed periods. To be sure, considerably improved values of T and P resulted from this procedure, but the police commissioner was never confronted with specifying them. The derived rescheduling was implemented in its entirety, approximately one month after the study was completed [LARS 72a].

The sad ending is associated with training of personnel. Approximately 8 years after the analysis reported here, insufficient training of 911 operators resulted in widely publicized inadequate response to several high-priority calls. Fully 121 operators were subsequently transferred to other duties (Figure 8. 1). Thus, the successful operation of any system requires continued professional training of personnel. This is just as true for model users as for 911 operators; Section 8.3 offers some suggestions for the training of model users.