Ph.D Student | Zeltyn Sergey |
---|---|

Subject | Call Centers with Impatient Customers: Exact Analysis and Many-server Asymptotics of the M/M/n+G Queue |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Emeritus Avishai Mandelbaum |

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.

First, we provide an extensive
background on the M/M/*n*+G model. The following research is motivated by
a phenomenon that has been observed in call center data: a clear linear
relation between the probability to abandon P{Ab} and average waiting time E[*W*].
We analyze its robustness within the framework of the M/M/*n*+G queue,
which gives rise to further theory and empirically-driven experiments .

Then three asymptotic operational
regimes for medium to large call centers are introduced and studied. These
regimes correspond to the following three staffing rules, as λ
and *n* increase indefinitely and μ held fixed :

**Efficiency-Driven (ED):** n
≈ (λ/μ) · (1-γ), γ>0,

**Quality-Driven (QD):** n
≈ (λ/μ) · (1+γ), γ>0,
and

**Quality and Efficiency Driven (QED):** n ≈ λ/μ + β (λ/μ)^{1/2},
-∞<β<∞.

In the ED regime, the probability to abandon and average wait converge to constants. In the QD regime, we observe a very high performance 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.

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. In turn, the much
simpler ED approximations are very useful for overloaded queueing systems . At the end, our theoretical results are applied to
call-by-call data of a large bank.