Name
Title | ||
|---|---|---|
Entropy maximization and NT vacation M/G/1 model with a startup and unreliable server: comparative analysis on the first two moments of system size |
Abstract | ||
|---|---|---|
We consider the control policy of an M/G/1 queueing system with a startup and unreliable server, in which the length of the vacation period is controlled either by the number of arrivals during the idle period, or by a timer. After all the customers have been served in the queue, the server immediately takes a vacation and operates an NT vacation policy: the server reactivates as soon as the number of arrivals in the queue reaches a predetermined threshold N or when the waiting time of the leading customer reaches T units. In such a variant vacation system, the steady-state probabilities cannot be obtained explicitly. Thus, the maximum entropy principle is used to derive the approximate formulas for the steady-state probability distributions of the queue length. A comparitive analysis of two approximation approaches, using the first and the second moments of system size, is studied. Both solutions are compared with the exact results under several service time distributions with specific parameter values. Our numerical investigations demonstrate that the use of the second moment of system size for the available information is, in general, sufficient to obtain more accurate estimations than that of the first moment. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1080/00207160701694161 | Int. J. Comput. Math. |
Keywords | Field | DocType |
server reactivates,entropy maximization,variant vacation system,system size,control policy,idle period,comparative analysis,unreliable server,queue length,nt vacation policy,vacation period,queueing system,bisection algorithm,maximum entropy | Applied mathematics,Mathematical optimization,M/D/1 queue,G/G/1 queue,Entropy maximization,Queue,M/G/k queue,Real-time computing,Probability distribution,Moment (mathematics),Principle of maximum entropy,Mathematics | Journal |
Volume | Issue | ISSN |
86 | 4 | 0020-7160 |
Citations | PageRank | References |
0 | 0.34 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jau-Chuan Ke | 1 | 348 | 44.17 |
| Chuen-Horng Lin | 2 | 231 | 15.93 |
| Hsin-I. Huang | 3 | 43 | 5.05 |