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    LIE-FERN HSUCHARLES S. TAPIEROCINHO LINNetwork of queues modeling in flexiblemanufacturing systems : a surveyRevue franaise dautomatique, dinformatique et de rechercheoprationnelle. Recherche oprationnelle, tome 27, no 2 (1993),p. 201-248.

    AFCET, 1993, tous droits rservs.

    Laccs aux archives de la revue Revue franaise dautomatique, dinfor-matique et de recherche oprationnelle. Recherche oprationnelle impliquelaccord avec les conditions gnrales dutilisation ( Toute utilisation commerciale ou impression systmatique estconstitutive dune infraction pnale. Toute copie ou impression de ce fi-chier doit contenir la prsente mention de copyright.

    Article numris dans le cadre du programmeNumrisation de documents anciens mathmatiques

  • Recherche oprationnelle/Oprations Research

    (vol. 27, n 2, 1993, p. 201 248)


    by Lie-Fern Hsu C1), Charles S. TAPIERO (2) and Cinho LIN (3)

    Abstract. - Queueing theory in the past and stiil to-day, been used intensively for the designand the analysis of Flexible Manufacturing Systems (FMS's). The queueing approach, combineson the one hand important theoretical developments in queueing theory and network of queues andextensive applications to the performance analysis of information Systems. Thepurpose ofthis paperis to survey the application of queues to the modelling of FMS's and to the management of suchmanufacturing Systems, based on the stochastic environment presumed by networks of queues.

    Keywords: Queues; Networks; Flexible Manufacturing Systems.

    Rsum. -Les files d'attentes ont t par le pass et sont jusqu' aujourd'hui utilises intensmentpour la conception et l'analyse d'ateliers flexibles. Les approches utilises combinent d'une part unnombre important d'tudes faites partir des processus stochastiques et les rseaux dfiles d'attenteet des applications aux systmes informatiques. Le but de cet article est de rsumer Vapplicationdes files d'attentes la modlisation des ateliers flexibles et aux problmes de gestion industriellequ'ils engendrent.

    Mots cls : Files d'attentes; Rseaux; Ateliers flexibles.


    Queueing models have been extensively used for the analysis and thedesign of flexible manufacturing Systems (FMS), recognizing on the onehand the simultaneity of job flows in a manufacturing job shop and onthe other the stochastic characteristic of job flows and process times. Asa resuit, impetus is now given to research and mostly applications ofqueueing theory in manufacturing (following an earlier use of queueingmodels in oprations management, Morse, 1963; Prabhu, 1965; Schrage,1968, 1970, 1974; Schrage and Miller, 166; Jackson, 1957, 1963; Gordon

    (*) Received july 1991.(*) Department of Management Baruch College, The City University of New York.(2) Department of Production Logistics, and Information Systems and Dcisions, ESSEC, Cergy

    Pontoise, France.(3) Department of Industrial Management Science National Cheng Kung University, Taiwan,

    Republic of China.

    Recherche oprationnelle/Oprations Research, 0399-0559/93/02 201 48/$ 6.80 AFCET-Gauthier-Vllars

  • 202 Lm-FERN Hsu et al

    and Newell, 1967; Conway et al, 1967; Cooper, 1972; Newell, 1971, 1980;Kleinrock, 1976; and the extensive bibliographical list in Crabill, Gross andMagazine, 1977). Additional rfrences for such applications abound and arepartially listed in many rfrences at the end of this paper. Authors suchas Sobel, Buzacott, Shanthikumar, Solberg, Stecke, Dubois, Yao, Stidham,Yechiali, Kekre, Hsu, Tapiero and others (see section 2) have made additionalcontributions to the analysis and design of manufacturing Systems. A surveyis given by Buzacott and Yao (1986) for example on the modeling of FMSusing queueing.

    Along with simulation, networks of queues provide a modeling frameworkwhich is practically helpful to the design and analysis of manufacturing sys-tems. Particularly, preliminary models based on tractable queueing networkscan provide a departure point for the study of far more complex modelsthrough simulation, providing thereby validation for these complex models.

    Application of networls of queues (assuming some strong assumptionsregarding the manufacturing process) can provide steady state performancemeasures regarding machines (or machine group) utilization, expected pro-duction rates, mean queue lengths, bottlenecks dtection, etc. For example, ithas been used to improve the grouping of oprations in a job shop (combinedwith group technology principles) and thus a rationality for the layout of FMSfacilities (Co, Wu and Reisman, 1988).

    Even though FMS s are Systems which are extremely well controlled andtherefore cannot be viewed as stochastic, the usefulness of network ofqueues orignates in the fact that over widely varying demand/load rangesand multiplicity of part types processed, the manufacturing system behaveson the aggregate as if it were subject to a stochastic behavior which is notalways captured by traditional models.

    Today it is agreed that disturbances such as breakdowns, fluctuatingdemand patterns, quality control, maintenance, etc. should be managed andreduced to render the production process a continuous flawless flow process,integrated and coordinated into a viable whole. To study these effects and theissues of designing, for example, capacity plans, basic sheduling rules, buffercapacity, loading/unloading machinery, etc., and managing them, queueingmodels may be extremely useful.

    They may be needed to provide insights regarding the long run responseof a manufacturing system to a given set of operating conditions and apreliminary apprciation of the managerial procedures used in the controlof oprations.

    Recherche oprationnelle/Oprations Research


    On the down side, these models which are difficult to analyze, particularlywhen reasonable assumptions are made regarding the manufacturing process(such as non-Poisson jobs arrivais, limited buffer capacities, applicationof scheduling techniques seeking to improve System's performance, batcharrivai, breakdowns and unreliabilities as well as the relative importance ofset-up time and costs in manufacturing Systems which are apparently not asimportant in computer Systems). Further, job shops managed for the mostpart in real time and which are subject to continuai changes in work ordersand plans cannot be analyzed by queueing models without a critical viewof such results. For these resons, an overall apprciation of what queueingtheory and its approximations can do for manufacturing Systems, is bothuseful and needed for FMS analysts (although a wide variety of approachesare developed which seem to relieve some of the difficulties encounteredwhen using queueing models. For example, refer to Ho and Cao, 1983;and Cassandra, 1984 and Ho (1985) for an extensive literature survey onPerturbation Analysis).

    The purpose of this paper is to provide an outline of queueing-networksmodeling in manufacturing and provide a classification which can be used toguide the FMS researcher and planner to what is known and not knownin queueing analysis for FMS management. We begin first by a simpledescriptive view of queue-like manufacturing cells which are then generalizedto a network of queues. Then we review a large number of published papersbased on queueing networks.


    2.1. Modeling a manufacturing cel! (station)

    The fondamental lments of a queue-like manufacturing cell can bedescribed by the external input process (or the arrivai pattern), the bufferarea, loading (i. e. the rule by which jobs leave the waiting line and enterfor service) as well as the service pattern which expresses how jobs areprocessed or manufactured (in terms of time, service capacity and the numberof servers). The essential ingrdients of a manufacturing cell are representedin Figure 1 which is self explanatory.

    To use queueing theory, however, it is necessary that we characterizemodels by basic constituent lments about which spcifie assumptions aremade. The specificity of these assumptions may render the model tractable,while limiting their generality. These lments are defined below.

    vol. 27, n 2 1993

  • 204 LIE-FERN HSU et ah

    L o a d i

    Buffer Queue

    Fini te or In f i n i t e

    By p r i o r i t yO p e n - l o o p v s . C l o s e d - l o o pF i xed Co s t s /Time

    P a t t e r n ofJ o b Ar r i val s

    Det e rmini st icS t o c h a st ic

    - Po i sson- G e n e r a l

    S i n g l e typeMul t i p 1 e typesCon t r o I led

    G G C3 G D C] Manufa c t ur i ngFac i 1 i t y Exit

    Jobs Outputand Routingt o Ot herDes t i nat ions

    S e r v i c i n g P a t t e r nDe t e r m i n i s t i cS t o c h a s t i c

    - Ex ponen t i a 1- G e n e r a l

    S i m p l e v s . M u l t i p l e M a c h i n e s

    By t y p e :-Ma c h i ni n g- P r o c e s s i n g- A s s embl y- I n s p e c t i o n-Ma t e r i a l H a n d l i n g

    Br e a k d o w n / N o Breakdown

    Er r o r Prone or Not

    Figure 1. - A queue-Iike manufacturing cell.

    2.1.1. Input Process or Arrivai Pattern (I)

    The arrivai pattern or input to a queueing System is often measured by themean inter arrivai time. In gnerai, we use M to symbolize Poisson input,and G to symbolize a gnerai input. For example, the following notationsare used:

    D, a deterministic int