Computational Procedures for a Class of GI/D/k Systems in Discrete Time
A class of discrete time GI/D/k systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2009/716364 |
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| author | Md. Mostafizur Rahman Attahiru Sule Alfa |
| author_facet | Md. Mostafizur Rahman Attahiru Sule Alfa |
| author_sort | Md. Mostafizur Rahman |
| collection | DOAJ |
| description | A class of discrete time GI/D/k
systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD) type Markov chain. It is shown that this transformed GI/D/1
system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures. |
| format | Article |
| id | doaj-art-66e10f6593304224acee3abf84af5a00 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-66e10f6593304224acee3abf84af5a002025-02-03T06:05:20ZengWileyJournal of Probability and Statistics1687-952X1687-95382009-01-01200910.1155/2009/716364716364Computational Procedures for a Class of GI/D/k Systems in Discrete TimeMd. Mostafizur Rahman0Attahiru Sule Alfa1Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, CanadaDepartment of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, CanadaA class of discrete time GI/D/k systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD) type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures.http://dx.doi.org/10.1155/2009/716364 |
| spellingShingle | Md. Mostafizur Rahman Attahiru Sule Alfa Computational Procedures for a Class of GI/D/k Systems in Discrete Time Journal of Probability and Statistics |
| title | Computational Procedures for a Class of GI/D/k Systems in Discrete Time |
| title_full | Computational Procedures for a Class of GI/D/k Systems in Discrete Time |
| title_fullStr | Computational Procedures for a Class of GI/D/k Systems in Discrete Time |
| title_full_unstemmed | Computational Procedures for a Class of GI/D/k Systems in Discrete Time |
| title_short | Computational Procedures for a Class of GI/D/k Systems in Discrete Time |
| title_sort | computational procedures for a class of gi d k systems in discrete time |
| url | http://dx.doi.org/10.1155/2009/716364 |
| work_keys_str_mv | AT mdmostafizurrahman computationalproceduresforaclassofgidksystemsindiscretetime AT attahirusulealfa computationalproceduresforaclassofgidksystemsindiscretetime |