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The Erlang A model--an M/M/s queue with exponential abandonment--is oftenused to represent a service system with impatient customers. For this system,the popular square-root staffing rule determines the necessary staffing levelto achieve the desirable QED (quality-and-efficiency-driven) service regime;however, the rule also implies that properties of large systems are highlysensitive to parameters. We reveal that the origin of this high sensitivity isdue to the operation of large systems at a point of singularity in a phasediagram of service regimes. We can avoid this singularity by implementing acongestion-based control (CBC) scheme--a scheme that allows the system tochange its arrival and service rates under congestion. We analyze a modifiedErlang A model under the CBC scheme using a Markov chain decomposition method,derive non-asymptotic and asymptotic normal representations of performanceindicators, and confirm that the CBC scheme makes large systems less sensitivethan the original Erlang A model.

Controlling arrival and service rates to reduce sensitivity of queueing systems with customer abandonment