Technical Note—What’s in a Constraint? On the Ambiguity of Standard Delay Targets

Ambiguities in Average Speed of Answer Targets Staffing problems are often formulated as satisfization problems, in which the cost of servers is minimized subject to quality of service constraints. These constraints are intended to capture customers’ disutility from waiting or, at least, its structure. In “What’s in a constraint? On the ambiguity of standard delay targets,” Soh and Gurvich show that such targets—especially the popular average speed of answer—are ambiguous: they give rise to multiple optimal solutions (prioritization policies), each consistent with different assumptions about how customers value their time. By choosing, among all optimal solutions, the one that minimizes a weighted index of diversion (a generalization of variance for the multiclass queue), a service provider can ensure that its ASA-based staffing and prioritization decisions align with a convex model of customer delay disutility. Nonambiguity can also be enforced by restricting attention to fixed queue ratio priority policies.