NDLI: Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue

Content Provider	Springer Nature Link
Author	Zeltyn, Sergey Mandelbaum, Avishai
Copyright Year	2005
Abstract	The subject of the present research is the M/M/n + G queue. This queue is characterized by Poisson arrivals at rate λ, exponential service times at rate μ, n service agents and generally distributed patience times of customers. The model is applied in the call center environment, as it captures the tradeoff between operational efficiency (staffing cost) and service quality (accessibility of agents).In our research, three asymptotic operational regimes for medium to large call centers are studied. These regimes correspond to the following three staffing rules, as λ and n increase indefinitely and μ held fixed: Efficiency-Driven (ED): $$n\ \approx \ (\lambda / \mu)\cdot (1 - \gamma),\gamma > 0,$$ Quality-Driven (QD): $$n \ \approx \ ( \lambda / \mu)\cdot (1 + \gamma),\gamma > 0$$ , and Quality and Efficiency Driven (QED): $$ n \ \approx \ \lambda/ \mu+\beta \sqrt{\lambda/\mu},-\infty < \beta < \infty $$ . In the ED regime, the probability to abandon and average wait converge to constants. In the QD regime, we observe a very high service level at the cost of possible overstaffing. Finally, the QED regime carefully balances quality and efficiency: agents are highly utilized, but the probability to abandon and the average wait are small (converge to zero at rate 1/ $$\sqrt{n}$$ ).Numerical experiments demonstrate that, for a wide set of system parameters, the QED formulae provide excellent approximation for exact M/M/n + G performance measures. The much simpler ED approximations are still very useful for overloaded queueing systems.Finally, empirical findings have demonstrated a robust linear relation between the fraction abandoning and average wait. We validate this relation, asymptotically, in the QED and QD regimes.
Starting Page	361
Ending Page	402
Page Count	42
File Format	PDF
ISSN	02570130
Journal	Queueing Systems
Volume Number	51
Issue Number	3-4
e-ISSN	15729443
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	queueing theory telephone call centers abandonment reneging impatience quality and efficiency-driven approximations Erlang-A Computer Communication Networks Systems Theory, Control Probability Theory and Stochastic Processes Operations Research/Decision Theory Production/Logistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue