Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup
Tóm tắt
This paper deals with the 〈N,p〉-policy M/G/1 queue with server breakdowns and general startup times, where customers arrive to demand the first essential service and some of them further demand a second optional service. Service times of the first essential service channel are assumed to follow a general distribution and that of the second optional service channel are another general distribution. The server breaks down according to a Poisson process and his repair times obey a general distribution in the first essential service channel and second optional service channel, respectively. The server operation starts only when N (N≥1) customers have accumulated, he requires a startup time before each busy period. When the system becomes empty, turn the server off with probability p (p∈[0,1]) and leave it on with probability (1−p). The method of maximum entropy principle is used to develop the approximate steady-state probability distribution of the queue length in the M/G(G, G)/1 queueing system. A study of the derived approximate results, compared to the established exact results for three different 〈N,p〉-policy queues, suggests that the maximum entropy principle provides a useful method for solving complex queueing systems.
Tài liệu tham khảo
Al-Jararha, J., Madan, K.C.: An M/G/1 queue with second optional service with general service time distribution. Inf. Manag. Sci. 14, 47–56 (2003)
Arizono, I., Cui, Y., Ohta, H.: An analysis of M/M/S queueing systems based on the maximum entropy principle. J. Oper. Res. Soc. 42, 69–73 (1991)
Baker, K.R.: A note on operating policies for the queue M/M/1 with exponential startup. INFOR 11, 71–72 (1973)
Bell, C.E.: Characterization and computation of optimal policies for operating an M/G/1 queueing system with removable server. Oper. Res. 19, 208–218 (1971)
Borthakur, A., Medhi, J., Gohain, R.: Poisson input queueing systems with startup time and under control operating policy. Comput. Oper. Res. 14, 33–40 (1987)
El-Affendi, M.A., Kouvatsos, D.D.: A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium. Acta Inform. 19, 339–355 (1983)
Feinberg, E.A., Kim, D.J.: Bicriterion optimization of an M/G/1 queue with a removable server. Probab. Eng. Inf. Sci. 10, 57–73 (1996)
Heyman, D.P.: Optimal operating policies for M/G/1 queueing system. Oper. Res. 16, 362–382 (1968)
Hur, S., Paik, S.J.: The effect of different arrival rates on the N-policy of M/G/1 with server setup. Appl. Math. Model. 23, 289–299 (1999)
Kim, D.J., Moon, S.A.: Randomized control of T-policy for an M/G/1 system. Comput. Ind. Eng. 51, 684–692 (2006)
Kouvatsos, D.D.: A maximum entropy analysis of the G/G/1 queue at equilibrium. J. Oper. Res. Soc. 39, 183–200 (1988)
Lee, H.W., Park, J.O.: Optimal strategy in N-policy production system with early set-up. J. Oper. Res. Soc. 48, 306–313 (1997)
Madan, K.C.: An M/G/1 queue with second optional service. Queueing Syst. 34, 37–46 (2000)
Medhi, J.: A single server Poisson input queue with a second optional channel. Queueing Syst. 42, 239–242 (2002)
Medhi, J., Templeton, J.G.C.: A Poisson input queue under N-policy and with a general start up time. Comput. Oper. Res. 19, 35–41 (1992)
Shore, J.E.: Derivation of equilibrium and time-dependent solutions to M/M/∞/N and M/M/∞ queueing systems using entropy maximization. In: Proceedings, National Computer Conference, AFIPS, pp. 483–487 (1978)
Shore, J.E.: Information theoretic approximations for M/G/1 and G/G/1 queueing systems. Acta Inf. 17, 43–61 (1982)
Tadj, L., Hamdi, A.: Maximum entropy solution to a quorum queueing system. Math. Comput. Model. 34, 19–27 (2001)
Takagi, H.: M/G/1/K queues with N-policy and setup times. Queueing Syst. 14, 79–98 (1993)
Wang, J.: An M/G/1 queue with second optional service and server breakdowns. Comput. Math. Appl. 47, 1713–1723 (2004)
Wang, K.-H., Ke, J.-C.: A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity. Appl. Math. Model. 24, 899–914 (2000)
Wang, K.-H., Ke, J.-C.: Control policies of an M/G/1 queueing system with a removable and non-reliable server. Int. Trans. Oper. Res. 9, 195–212 (2002)
Wang, K.-H., Wang, T.-Y., Pearn, W.L.: Maximum entropy analysis to the N policy M/G/1 queueing system with server breakdowns and general startup times. Appl. Math. Comput. 165, 45–61 (2005)
Wang, K.-H., Wang, T.-Y., Pearn, W.L.: Optimal control of the N policy M/G/1 queueing system with server breakdowns and general startup time. Appl. Math. Model. 31, 2199–2212 (2007)
Wu, J.S., Chan, W.C.: Maximum entropy analysis of multiple-server queueing systems. J. Oper. Res. Soc. 40, 815–825 (1989)
Yadin, M., Naor, P.: Queueing systems with a removable service station. Oper. Res. Q. 14, 393–405 (1963)