The lagged PSA for estimating peak congestion in multiserver Markovian queues with periodic arrival rates
Article Abstract:
A revised simple peak hour approximation (SPHA) is proposed for the estimation of peak congestion in multiserver queuing systems having exponential service times and time-changing periodic Poisson intervals. Derivation of this lagged pointwise stationary approximation (lagged PSA) involves estimation of the time of the actual peak congestion by the time of peak congestion in an infinite server model, followed by substitution of the arrival rate at this time in the corresponding stationary finite server model. The lagged PSA is demonstrated to be frequently more precise than the SPHA and to lead to significantly smaller errors when average service times are larger than a half an hour. Lastly, the lagged PSA correctly determines appropriate staffing levels to achieve targeted performance levels to maintain low congestion.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1997
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On the efficiency of imbalance in multi-facility multi-server service systems
Article Abstract:
An analysis is performed to examine the problem of the simultaneous allocation of servers and demands in multi-facility multi-server service systems for an optimal system peformance measure. It is assumed that the demand stream is homogeneous and has uniform service time distribution that is free from the influence of the server or the facility. Simple approximations and numerical results demonstrate that uneven allocation of indidivual facilities enhances the overall efficiency of a multi-facility system with Poisson arrivals. Findings reveal that, for any given number of facilities and a specified number of servers, server assignment is optimal if it is maximal according to the partial order of majorization.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1995
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A note on approximating peak congestion in M(sub t)/G/infinity queues with sinusoidal arrivals
Article Abstract:
A study was conducted to analyze the M(sub t)/G/infinity queue wherein the arrivals of customers at service facilities correlate with a sinusoidal Poisson process. The sinusoidal Poisson process supports an arrival rate given by the amplitude of the arrival function and period. Two factors were found to influence the accuracy of the approximation, namely, the service rate and the relative amplitude. In addition, congestion resulting from the peak epoch that occurs after the peak in the arrival rate function was analyzed. Results indicated that the anticipated number of customers during peak congestion can be estimated based on service distributions supporting a coefficient of variation between 0 and 1.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1998
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