Two Issues in Setting Call Centre Staffing Levels

Motivated by a problem facing the Police Communication Centre in Auckland, New Zealand, we consider the setting of staffing levels in a call centre with priority customers. The choice of staffing level over any particular time period (e.g., Monday from 8 am–9 am) relies on accurate arrival rate information. The usual method for identifying the arrival rate based on historical data can, in some cases, lead to considerable errors in performance estimates for a given staffing level. We explain why, identify three potential causes of the difficulty, and describe a method for detecting and addressing such a problem.

[1]  D. Freedman.  Poisson Processes with Random Arrival Rate , 1962 .

[2]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[3]  Richard H. Davis.  Waiting-Time Distribution of a Multi-Server, Priority Queuing System , 1966, Oper. Res..

[4]  J. Kingman.  A FIRST COURSE IN STOCHASTIC PROCESSES , 1967 .

[5]  Alan J. Rolfe.  A Note on Marginal Allocation in Multiple-Server Service Systems , 1971 .

[6]  M. E. Dyer,et al.  Note---On the Validity of Marginal Analysis for Allocating Servers in M/M/c Queues , 1977 .

[7]  T. Rolski.  Queues with non-stationary input stream: Ross's conjecture , 1981, Advances in Applied Probability.

[8]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[9]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[10]  W. Grassmann.  The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity , 1983 .

[11]  Hau L. Lee,et al.  A note on the convexity of performance measures of M/M/c queueing systems , 1983 .

[12]  Richard R. Weber,et al.  Technical Note - A Note on Waiting Times in Single Server Queues , 1983, Oper. Res..

[13]  Hillel Kumin,et al.  Technical Note - A Convexity Result for a Class of GI/G/1 Queueing Systems , 1983, Oper. Res..

[14]  U. Yechiali,et al.  Waiting Times in the Non-Preemptive Priority M/M/c Queue , 1985 .

[15]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[16]  Tomasz Rolski,et al.  Upper Bounds for Single Server Queues with Doubly Stochastic Poisson Arrivals , 1986, Math. Oper. Res..

[17]  Paul H. Zipkin,et al.  Strong Convexity Results for Queueing Systems , 1987, Oper. Res..

[18]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .

[19]  Arie Harel,et al.  Convexity Properties of the Erlang Loss Formula , 1990, Oper. Res..

[20]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[21]  Ward Whitt,et al.  Numerical Inversion of Laplace Transforms of Probability Distributions , 1995, INFORMS J. Comput..

[22]  Ward Whitt,et al.  Dynamic staffing in a telephone call center aiming to immediately answer all calls , 1999, Oper. Res. Lett..

[23]  Stephen E. Chick,et al.  Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty , 2001, Oper. Res..

[24]  Peter J. Kolesar,et al.  Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands , 2001, Oper. Res..