Two finite-difference methods for solving MAP(t)/PH(t)/1/K queueing models |
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Authors: | Dormuth Darryl Wayne Alfa Attahiru Sule |
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Institution: | (1) Department of Mechanical and Industrial Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2 |
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Abstract: | In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing model are introduced, one based on the Backwards Euler Method and the other on the Uniformization Method. Both methods
use finite-differencing with a discretized, adaptive time-mesh to obtain time-dependent values for the entire state probability
vector. From this vector, most performance parameters such as expected waiting time and expected number in the system can
be computed. Also presented is a technique to compute the entire waiting (sojourn) time distribution as a function of transient
time. With these two solution methods one can examine any transient associated with the MAP(t)/PH(t)/1/K model including time-varying arrival and/or service patterns. Four test cases are used to demonstrate the effectiveness of
these methods. Results from these cases indicate that both methods provide fast and accurate solutions to a wide range of
transient scenarios.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | transient solutions finite-difference uniformization method Markov arrival process phase-type distribution waiting time distribution time-varying queueing parameters |
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