Classification of queueing models for a workstation with interruptions: a review

Queueing theory is commonly used to evaluate the performance of production systems. Due to the complexity of practical production lines, choosing correct queueing models under the existence of interruptions can be intricate, but is critical to the evaluation of system performance. This paper gives a review of research in this area, proposes a systematic way to classify different types of interruptions in manufacturing systems and suggests proper queueing models for each category. The operational definition of service time is given and the decomposition properties for the run-based state-induced and time-based preemptive events are explained. The corresponding G/G/1 approximate models are proposed.

[1]  G. F. Newell.  Approximate Behavior of Tandem Queues , 1979 .

[2]  Ciro D'Apice,et al.  Queueing Theory , 2003, Operations Research.

[3]  Leon F. McGinnis,et al.  Queueing models for single machine manufacturing systems with interruptions , 2008, 2008 Winter Simulation Conference.

[4]  Hamid Reza Golmakani.  Condition-based inspection scheme for condition-based maintenance , 2012 .

[5]  Peter D. Welch,et al.  On a Generalized M/G/1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service , 1964 .

[6]  Jürgen Branke,et al.  Setup-oriented dispatching rules – a survey , 2012 .

[7]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[8]  Kathryn E. Stecke,et al.  REVIEW OF OPERATOR/MACHINE INTERFERENCE MODELS. , 1985 .

[9]  Wolfgang Kraemer,et al.  Approximate Formulae for the Delay in the Queueing System GI/G/ 1 , 1976 .

[10]  Leonard Kleinrock,et al.  A Queue with Starter and a Queue with Vacations: Delay Analysis by Decomposition , 1986, Oper. Res..

[11]  Marcel F. Neuts,et al.  A Markovian Queue with N Servers Subject to Breakdowns and Repairs , 1979 .

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

[13]  Bhaskar Sengupta,et al.  A Queue with Service Interruptions in an Alternating Random Environment , 1990, Oper. Res..

[14]  L. Christie,et al.  Queuing with Preemptive Priorities or with Breakdown , 1958 .

[15]  Hideaki Takagi,et al.  Analysis and Application of Polling Models , 2000, Performance Evaluation.

[16]  Awi Federgruen,et al.  Queueing Systems with Service Interruptions , 1986, Oper. Res..

[17]  D. P. Heyman.  A diffusion model approximation for the GI/G/1 queue in heavy traffic , 1975, The Bell System Technical Journal.

[18]  P. Naor,et al.  Some Queuing Problems with the Service Station Subject to Breakdown , 1963 .

[19]  Paulo Morelato França,et al.  Scheduling with Sequence-Dependent Setup Times and Early-Tardy Penalties , 1997 .

[20]  K. Thiruvengadam.  Queuing with Breakdowns , 1963 .

[21]  J. Keilson.  Queues Subject to Service Interruption , 1962 .

[22]  Fariborz Jolai,et al.  A novel hybrid meta-heuristic algorithm for a no-wait flexible flow shop scheduling problem with sequence dependent setup times , 2012 .

[23]  Søren Asmussen,et al.  Queueing Simulation in Heavy Traffic , 1992, Math. Oper. Res..

[24]  Jatinder N. D. Gupta,et al.  A REVIEW OF FLOWSHOP SCHEDULING RESEARCH WITH SETUP TIMES , 2000 .

[25]  Izhak Rubin,et al.  Polling with a General-Service Order Table , 1987, IEEE Trans. Commun..

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

[27]  Hideaki Takagi,et al.  Queuing analysis of polling models , 1988, CSUR.

[28]  Onno Boxma,et al.  On a queueing model with service interruptions , 2006 .

[29]  J. Kingman.  Some inequalities for the queue GI/G/1 , 1962 .

[30]  I. Adan,et al.  QUEUEING THEORY , 1978 .

[31]  N. K. Jaiswal,et al.  Priority queues , 1968 .

[32]  Mostafa Zandieh,et al.  Comparisons of bi-objective genetic algorithms for hybrid flowshop scheduling with sequence-dependent setup times , 2012 .

[33]  Kan Wu,et al.  The Determination and Indetermination of Service Times in Manufacturing Systems , 2008, IEEE Transactions on Semiconductor Manufacturing.

[34]  Leon F. McGinnis,et al.  Queueing models for a single machine subject to multiple types of interruptions , 2011 .

[35]  James R. Morrison,et al.  Practical Extensions to Cycle Time Approximations for the $G/G/m$-Queue With Applications , 2007, IEEE Transactions on Automation Science and Engineering.

[36]  Leon F. McGinnis,et al.  Interpolation approximations for queues in series , 2013 .

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

[38]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[39]  Martin Eisenberg,et al.  Queues with Periodic Service and Changeover Time , 1972, Oper. Res..

[40]  Lani Haque,et al.  A survey of the machine interference problem , 2007, Eur. J. Oper. Res..

[41]  J. A. Buzacott,et al.  Models of automatic transfer lines with inventory banks a review and comparison , 1978 .

[42]  Walter L. Smith.  On the distribution of queueing times , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[43]  D. V. Lindley,et al.  The theory of queues with a single server , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[44]  H. Ashcroft,et al.  The Productivity of Several Machines Under the Care of One Operator , 1950 .