A Queueing Model for Multi-product Production System Under Varying Manufacturing Environment

In this paper, we propose a queueing model for a multi-product production system in which the manufacturing environments are changing over time between some predetermined states. We model this system by the discrete-time Markovian Arrival Stream (MAS) and derive the mean level of WIP (work-in-process) inventory. A numerical example is presented.

[1]  Tetsuya Takine,et al.  Distributional Form of Little's Law for FIFO Queues with Multiple Markovian Arrival Streams and Its Application to Queues with Vacations , 2001, Queueing Syst. Theory Appl..

[2]  Tetsuya Takine,et al.  Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams , 2003 .

[3]  M. Neuts,et al.  A single-server queue with server vacations and a class of non-renewal arrival processes , 1990, Advances in Applied Probability.

[4]  J. Doob Stochastic processes , 1953 .

[5]  Tetsuya Takine,et al.  Subexponential asymptotics of the waiting time distribution in a single-server queue with multiple Markovian arrival streams , 2001 .

[6]  Tetsuya Takine,et al.  Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions , 2001, Queueing Syst. Theory Appl..

[7]  Tetsuya Takine,et al.  Analysis of an Infinite-Server Queue with Batch Markovian Arrival Streams , 2002, Queueing Syst. Theory Appl..

[8]  Marcel F. Neuts,et al.  Markov chains with marked transitions , 1998 .

[9]  Qi-Ming He,et al.  Queues with marked customers , 1996, Advances in Applied Probability.

[10]  Tetsuya Takine,et al.  The workload in the MAP/G/1 queue with state-dependent services: its application to a queue with preemptive resume priority , 1994 .

[11]  Tetsuya Takine,et al.  Matrix Product-Form Solution for an LCFS-PR Single-Server Queue with Multiple Arrival Streams Governed by a Markov Chain , 2002, Queueing Syst. Theory Appl..

[12]  Bong Dae Choi,et al.  Discrete Time Queues with Markovian Arrival Streamsand State-Dependent Service Times(Fundamental Theories) , 2003 .

[13]  Attahiru Sule Alfa,et al.  The $$MMAP\left[ K \right]/PH\left[ K \right]/1$$ queues with a last-come-first-served preemptive service discipline , 1998, Queueing Syst. Theory Appl..

[14]  Hiroyuki Masuyama,et al.  STATIONARY QUEUE LENGTH IN A FIFO SINGLE SERVER QUEUE WITH SERVICE INTERRUPTIONS AND MULTIPLE BATCH MARKOVIAN ARRIVAL STREAMS , 2003 .

[15]  S. Asmussen,et al.  Marked point processes as limits of Markovian arrival streams , 1993 .

[16]  Tetsuya Takine A RECENT PROGRESS IN ALGORITHMIC ANALYSIS OF FIFO QUEUES WITH MARKOVIAN ARRIVAL STEAMS , 2001 .