TY - JOUR

T1 - When to arrive at a queue with earliness, tardiness and waiting costs

AU - Sherzer, Eliran

AU - Kerner, Yoav

N1 - Funding Information:
Thanks are due to Tomer Sharon for generating numerical examples and Joseph Kreimer for making helpful comments. Also, we wish to thank the editor and reviewers for their thorough work and meaningful suggestions. This research is supported by the Israel Science Foundation , Grant No. 1319/11 .
Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We consider a queueing facility where customers decide when to arrive. All customers have the same desired arrival time (w.l.o.g. time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer wishes to minimize the sum of three costs: earliness, tardiness and waiting. We assume that all three costs are linear with time and are defined as follows. Earliness is the time between arrival and time zero, if there is any. Tardiness is simply the time of entering service, if it is after time zero. Waiting time is the time from arrival until entering service. We focus on customers’ rational behavior, assuming that each customer wants to minimize his total cost, and in particular, we seek a symmetric Nash equilibrium strategy. We show that such a strategy is mixed, unless trivialities occur. We construct a set of equations that its solution provides the symmetric Nash equilibrium. The solution is a continuous distribution on the real line. We also compare the socially optimal solution (that is, the one that minimizes total cost across all customers) to the overall cost resulting from the Nash equilibrium.

AB - We consider a queueing facility where customers decide when to arrive. All customers have the same desired arrival time (w.l.o.g. time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer wishes to minimize the sum of three costs: earliness, tardiness and waiting. We assume that all three costs are linear with time and are defined as follows. Earliness is the time between arrival and time zero, if there is any. Tardiness is simply the time of entering service, if it is after time zero. Waiting time is the time from arrival until entering service. We focus on customers’ rational behavior, assuming that each customer wants to minimize his total cost, and in particular, we seek a symmetric Nash equilibrium strategy. We show that such a strategy is mixed, unless trivialities occur. We construct a set of equations that its solution provides the symmetric Nash equilibrium. The solution is a continuous distribution on the real line. We also compare the socially optimal solution (that is, the one that minimizes total cost across all customers) to the overall cost resulting from the Nash equilibrium.

UR - http://www.scopus.com/inward/record.url?scp=85032385911&partnerID=8YFLogxK

U2 - 10.1016/j.peva.2017.08.010

DO - 10.1016/j.peva.2017.08.010

M3 - Article

AN - SCOPUS:85032385911

VL - 117

SP - 16

EP - 32

JO - Performance Evaluation

JF - Performance Evaluation

SN - 0166-5316

ER -