On the advantage of being the first server
Article Abstract:
The impact of revealing or concealing queue lengths on the profits of competing servers is considered. The problem involves the determination of equilibrium threshold strategies of customers and their impact on the utilization of two servers with separate queues. The first queue may be observed by arriving customers while the second is concealed from customers. It is illustrated with the case of two gas stations in a street and customers who decide which queue to join based on their observations of the queue length at the first gas station. To determine whether the first station has an advantage over its rival, a model that characterizes the arrivals as Poisson processes and service utilization as exponential distributions is employed to solve for the ratio of the average arrival rate of the service system to the average joint service rate of the two servers, otherwise known as the utilization factor of the system.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1996
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Decentralized regulation of a queue
Article Abstract:
A study is conducted to examine the issue of the regulation of the arrival rate to a queueing system with exponential service and without balking. A queue without balking is one whose length is not revealed and which arriving customers decide to join based on previously gathered statistical data. In contrast, a queue with balking is one whose observable length determines the decision of incoming customers to join it or not. A decentralized self-regulating mechanism for queue regulation is analyzed. It is demonstrated that this mechanism influences the socially optimal process as well as the service order when the exponential service demand is uniform for all customers. The analysis also suggests that the profit maximizing service rate is the same as or lower than the socially optimal rate.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1995
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A Diffusion Approximation for an M/G/M Queue with Group Arrivals
Article Abstract:
The M/G/M queuing system with group arrivals is analyzed. A diffusion approximation is used to study steady-state behavior. Assumptions for this formulation are given. Data on the distribution of the number of customers, the delay probability, the mean queue length and the mean number of customers is included. Service time distributions are limited to single server queues. Numerical results compare the approximations with regard to number of servers.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1984
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