Controlling excessive waiting times in small service systems with time-varying demand: An extension of the ISA algorithm

In many service systems, the arrival pattern is not constant throughout the day. This raises the question how staffing decisions should be adapted in view of controlling customer's waiting times. Assuming a single-stage queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman et al. (2008). The main advantage of our extension is that it enables to control the probability of experiencing an excessive waiting time, in particular in small systems.

[1]  Baris Balcioglu,et al.  Approximations for the M/GI/N+GI type call center , 2008, Queueing Syst. Theory Appl..

[2]  WhittWard The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase , 1991 .

[3]  P. Kolesar,et al.  The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals , 1991 .

[4]  S. Zeger,et al.  The challenge of predicting demand for emergency department services. , 2008, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[5]  Ward Whitt,et al.  Server Staffing to Meet Time-Varying Demand , 1996 .

[6]  Mieke Defraeye,et al.  Setting Staffing Levels in Systems with Time-Varying Demand: The Context of an Emergency Department , 2011 .

[7]  Ward Whitt,et al.  Engineering Solution of a Basic Call-Center Model , 2005, Manag. Sci..

[8]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[9]  Avishai Mandelbaum,et al.  Designing a Call Center with Impatient Customers , 2002, Manuf. Serv. Oper. Manag..

[10]  Robert W. Day,et al.  Improving patient flow in a hospital through dynamic allocation of cardiac diagnostic testing time slots , 2010, Decis. Support Syst..

[11]  Linda V. Green,et al.  AN IMPROVED HEURISTIC FOR STAFFING TELEPHONE CALL CENTERS WITH LIMITED OPERATING HOURS , 2003 .

[12]  W. A. Massey,et al.  An Analysis of the Modified Offered-Load Approximation for the Nonstationary Erlang Loss Model , 1994 .

[13]  P. Kolesar,et al.  On the accuracy of the simple peak hour approximation for Markovian queues , 1995 .

[14]  Ward Whitt,et al.  Understanding the Efficiency of Multi-Server Service Systems , 1992 .

[15]  Mieke Defraeye,et al.  Controlling Excessive Waiting Times in Emergency Departments: An Extension of the ISA Algorithm , 2011 .

[16]  Ward Whitt,et al.  Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System , 2007 .

[17]  Randolph W. Hall,et al.  Modeling Patient Flows Through the Health care System , 2013 .

[18]  W. Whitt The pointwise stationary approximation for M 1 / M 1 / s , 1991 .

[19]  Avishai Mandelbaum,et al.  Service Engineering in Action: The Palm/Erlang-A Queue, with Applications to Call Centers , 2007 .

[20]  Ward Whitt,et al.  What you should know about queueing models to set staffing requirements in service systems , 2007 .

[21]  Avishai Mandelbaum,et al.  Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue , 2005, Queueing Syst. Theory Appl..

[22]  P Walley,et al.  Designing the accident and emergency system: lessons from manufacturing , 2003, Emergency medicine journal : EMJ.

[23]  D. L. Jagerman,et al.  Nonstationary blocking in telephone traffic , 1975, The Bell System Technical Journal.

[24]  Xudong Wu,et al.  A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline , 2007, INFORMS J. Comput..

[25]  Gregory Dobson,et al.  On the impact of analyzing customer information and prioritizing in a service system , 2011, Decis. Support Syst..

[26]  Ward Whitt,et al.  The Physics of the Mt/G/∞ Queue , 1993, Oper. Res..

[27]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

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

[29]  R. A. Green,et al.  Using queueing theory to increase the effectiveness of emergency department provider staffing. , 2006, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[30]  Ward Whitt,et al.  Peak congestion in multi-server service systems with slowly varying arrival rates , 1997, Queueing Syst. Theory Appl..

[31]  Ward Whitt,et al.  Staffing of Time-Varying Queues to Achieve Time-Stable Performance , 2008, Manag. Sci..

[32]  Ward Whitt,et al.  Heavy-Traffic Limits for Queues with Many Exponential Servers , 1981, Oper. Res..

[33]  Avishai Mandelbaum,et al.  Queueing Models of Call Centers: An Introduction , 2002, Ann. Oper. Res..

[34]  L. Graff,et al.  Emergency physician workload: a time study. , 1993, Annals of emergency medicine.