Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs

This paper is concerned with the optimal design of queueing systems. The main decisions in the design of such systems are the number of servers, the appropriate control to have on the arrival rates, and the appropriate service rate these servers should possess. In the formulation of the objective fu...

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Main Authors: PARLAR, Mahmut, MOOSA, Sharafali
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Language:English
Published: Institutional Knowledge at Singapore Management University 2014
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Online Access:https://ink.library.smu.edu.sg/lkcsb_research/3626
https://doi.org/10.1002/asmb.1983
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spelling sg-smu-ink.lkcsb_research-46252016-01-06T13:35:52Z Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs PARLAR, Mahmut MOOSA, Sharafali This paper is concerned with the optimal design of queueing systems. The main decisions in the design of such systems are the number of servers, the appropriate control to have on the arrival rates, and the appropriate service rate these servers should possess. In the formulation of the objective function to this problem, most publications use only linear cost rates. The linear rates, especially for the waiting cost, do not accurately reflect reality. Although there are papers involving nonlinear cost functions, no paper has ever considered using polynomial cost functions of degree higher than two. This is because simple formulas for computing the higher moments are not available in the literature. This paper is an attempt to fill this gap in the literature. Thus, the main contributions of our work are as follows: (i) the derivation of a very simple formula for the higher moments of the waiting time for the M/M/s queueing system, which requires only the knowledge of the expected waiting time; (ii) proving their convexity with respect to the design variables; and (iii) modeling and solving more realistic design problems involving general polynomial cost functions.We also focus on simultaneous optimization of the staffing level, arrival rate and service rate. 2014-07-01T07:00:00Z text https://ink.library.smu.edu.sg/lkcsb_research/3626 info:doi/10.1002/asmb.1983 https://doi.org/10.1002/asmb.1983 Research Collection Lee Kong Chian School Of Business eng Institutional Knowledge at Singapore Management University M/M/s queues higher moments of waiting time convexity design and optimization Operations and Supply Chain Management Operations Research, Systems Engineering and Industrial Engineering
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic M/M/s queues
higher moments of waiting time
convexity
design and optimization
Operations and Supply Chain Management
Operations Research, Systems Engineering and Industrial Engineering
spellingShingle M/M/s queues
higher moments of waiting time
convexity
design and optimization
Operations and Supply Chain Management
Operations Research, Systems Engineering and Industrial Engineering
PARLAR, Mahmut
MOOSA, Sharafali
Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs
description This paper is concerned with the optimal design of queueing systems. The main decisions in the design of such systems are the number of servers, the appropriate control to have on the arrival rates, and the appropriate service rate these servers should possess. In the formulation of the objective function to this problem, most publications use only linear cost rates. The linear rates, especially for the waiting cost, do not accurately reflect reality. Although there are papers involving nonlinear cost functions, no paper has ever considered using polynomial cost functions of degree higher than two. This is because simple formulas for computing the higher moments are not available in the literature. This paper is an attempt to fill this gap in the literature. Thus, the main contributions of our work are as follows: (i) the derivation of a very simple formula for the higher moments of the waiting time for the M/M/s queueing system, which requires only the knowledge of the expected waiting time; (ii) proving their convexity with respect to the design variables; and (iii) modeling and solving more realistic design problems involving general polynomial cost functions.We also focus on simultaneous optimization of the staffing level, arrival rate and service rate.
format text
author PARLAR, Mahmut
MOOSA, Sharafali
author_facet PARLAR, Mahmut
MOOSA, Sharafali
author_sort PARLAR, Mahmut
title Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs
title_short Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs
title_full Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs
title_fullStr Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs
title_full_unstemmed Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs
title_sort optimal design of multi-server markovian queues with polynomial waiting and service costs
publisher Institutional Knowledge at Singapore Management University
publishDate 2014
url https://ink.library.smu.edu.sg/lkcsb_research/3626
https://doi.org/10.1002/asmb.1983
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