On M/G/1 system under NT policies with breakdowns, startup and closedown

This paper studies the vacation policies of an M/G/1 queueing system with server breakdowns, startup and closedown times, in which the length of the vacation period is controlled either by the number of arrivals during the vacation period, or by a timer. After all the customers are served in the queue exhaustively, the server is shutdown (deactivates) by a closedown time. At the end of the shutdown time, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the closedown time. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. If some customers arrive during this closedown time, the service is immediately started without leaving for a vacation and without a startup time. We analyze the system characteristics for each scheme.

[1]  Jacques Teghem.  Optimal control of a removable server in an M/G/1 queue with finite capacity , 1987 .

[2]  Gang Chen,et al.  Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/Hk/1 Queueing System , 2004 .

[3]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..

[4]  Attahiru Sule Alfa,et al.  Discrete NT-policy single server queue with Markovian arrival process and phase type service , 1996 .

[5]  Kuo-Hsiung Wang,et al.  A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity , 2000 .

[6]  Attahiru Sule Alfa,et al.  Optimal (N, T)-policy for M/G/1 system with cost structures , 2000, Perform. Evaluation.

[7]  Kyung C. Chae,et al.  Batch arrival queue with N-policy and single vacation , 1995, Comput. Oper. Res..

[8]  K. H. Wang,et al.  (International Transactions in Operational Research,09(2):195-212)Control Policies of an M/G/1 Queueing System with a Removable and Non-reliable Server , 2002 .

[9]  Offer Kella.  The threshold policy in the M/G/1 queue with server vacations , 1989 .

[10]  B. D. Sivazlian,et al.  Distributions and first moments of the busy and idle periods in controllable M/G/1 Queueing Models with Simple and Dyadic Policies , 1995 .

[11]  Ying Hui Tang.  A single-server M/G/1 queueing system subject to breakdowns—some reliability and queueing problems , 1997 .

[12]  Daniel P. Heyman,et al.  The T-Policy for the M/G/1 Queue , 1977 .

[13]  Kuo-Hsiung Wang.  Optimal operation of a markovian queueing system with a removable and non-reliable server , 1995 .

[14]  Lotfi Tadj,et al.  On an M/G/1 quorum queueing system under T-policy , 2003, J. Oper. Res. Soc..

[15]  Zhisheng Niu,et al.  A finite‐capacity queue with exhaustive vacation/close‐down/setup times and Markovian arrival processes , 1999, Queueing Syst. Theory Appl..

[16]  Sun Hur,et al.  The effect of different arrival rates on the N-policy of M/G/1 with server setup , 1999 .

[17]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[18]  Sun Hur,et al.  An Analysis of M/G/1 System with N and T-Policy , 2003 .

[19]  Daniel P. Heyman,et al.  Optimal Operating Policies for M/G/1 Queuing Systems , 1968, Oper. Res..

[20]  Attahiru Sule Alfa,et al.  Optimal policies for M/M/m queue with two different kinds of (N, T)-policies , 2000 .

[21]  James G. C. Templeton,et al.  A poisson input queue under N-policy and with a general start up time , 1992, Comput. Oper. Res..

[22]  Hideaki Takagi.  M/G/1/K queues withN-policy and setup times , 1993, Queueing Syst. Theory Appl..

[23]  Mandyam M. Srinivasan,et al.  Control policies for the M X /g/ 1 queueing system , 1989 .

[24]  Jesús R. Artalejo.  Some results on the M/G/1 queue with N-policy , 1998 .

[25]  M. Yadin,et al.  Queueing Systems with a Removable Service Station , 1963 .

[26]  Ho Woo Lee,et al.  Optimal strategy in N-policy production system with early set-up , 1997 .

[27]  Kuo-Hsiung Wang,et al.  Optimal control of an M/Hk/1 queueing system with a removable server , 2003, Math. Methods Oper. Res..

[28]  Peter W. Jones,et al.  Stochastic Modelling and Analysis , 1988 .

[29]  D. Gaver.  A Waiting Line with Interrupted Service, Including Priorities , 1962 .

[30]  Raymond G. Vickson,et al.  The Optimal Service Policies In An M/G/1 Queueing System With Multiple Vacation Types , 2001 .

[31]  Kuo-Hsiung Wang,et al.  (Applied Mathematical Modelling,23(8):651-666)Optimal Control of a Removable and Non-reliable Server in an Infinite and a Finite M/H2/1 Queueing System , 1999 .

[32]  Do Le Minh,et al.  Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations , 1988 .

[33]  Hideaki Takagi.  Time-dependent process of M/G/1 vacation models with exhaustive service , 1992 .

[34]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[35]  Yutaka Takahashi,et al.  Queueing analysis: A foundation of performance evaluation, volume 1: Vacation and priority systems, Part 1: by H. Takagi. Elsevier Science Publishers, Amsterdam, The Netherlands, April 1991. ISBN: 0-444-88910-8 , 1993 .

[36]  Kuo-Hsiung Wang.  Optimal control of an M/Ek/1 queueing system with removable service station subject to breakdowns , 1997 .

[37]  Jau-Chuan Ke,et al.  The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns , 2003 .

[38]  U. Yechiali,et al.  Utilization of idle time in an M/G/1 queueing system Management Science 22 , 1975 .