@preamble{ "\newcommand{\noopsort}[1]{} " # "\newcommand{\printfirst}[2]{#1} " # "\newcommand{\singleletter}[1]{#1} " # "\newcommand{\switchargs}[2]{#2#1} " } @string{rrw="R.R. Weber"} @string{gw="G. Weiss"} @string{kg="Glazebrook, K.D."} @string{aap="Adv. Appl. Prob."} @string{jap="J. Appl. Prob."} @string{mor="Mathematics of Operations Research"} @string{ms="Management Science"} @string{om="Omega"} @string{or="Operations Research"} @string{naval="Naval Research Logistics Quarterly"} @string{peis="Probability in the Engineering and Informational Sciences"} @string{auto="IEEE Trans. Auto. Control"} @article{Ana87, author = {Anantharam, V.}, title = {Probabilistic proof of interchangeability of {$/M/1$} queues in series}, journal = {Queueing Systems, Theory and Application}, year = 1987, volume = {{\bf 2}}, pages = {387--392} } @article{Avi65, author = {Avi-Itzhak, B.}, title = {A Sequence of Service Stations with Arbitrary Input and Regular Service Times}, journal = ms, year = 1965, volume = {{\bf 11}}, pages = {565--573} } @phdthesis{Box77, author = {Boxma, O.}, title = {Analysis of Models for Tandem Queues}, year = 1977, school = {University of Utrecht}, type = {{Ph.D.} dissertation} } @article{Bur56, author = {Burke, P.J.}, title = {The Output of a Queueing System}, journal = or, year = 1956, volume = {{\bf 4}}, pages = {699--704} } @article{Cha89, author = {Chao, X. and Pinedo, M. and Sigman, K.}, title = {On the Interchangeability and Stochastic Ordering of Exponential Queues in Tandem with Blocking}, journal = peis, year = 1989, volume = {{\bf 3}}, pages = {223--236} } @article{Cha90b, author = {Chao, X. and Pinedo, M.}, title = {Batch Arrivals to a Tandem Queue Without an Intermediate Buffer}, journal = {Stochastic Models}, year = 1990, volume = {{\bf 6}}, pages = {735--748} } @article{Cha91d, author = {Chang, C-S. and Chao, X. and Pinedo, M.}, title = {Stochastic Convexity for Multi-Dimensional Processes and its Applications}, journal = {IEEE Transactions on Automatic Control}, year = 1991 } @article{Cha92b, author = {Chao, X. and Pinedo, M.}, title = {On the Reversibility of Tandem Queues with Blocking}, journal = { }, year = 1992 } @article{Din91, author = {Ding, J. and Greenberg, B.S.}, title = {Bowl shapes are better with buffers --- sometimes.}, journal = peis , year = 1991 } @article{Din91b, author = {Ding, J. and Greenberg, B.S.}, title = {Optimal order for servers in series with no queue capacity}, journal = peis, year = 1991, volume = {{\bf 5}}, pages = {449--462} } @article{Fol84, author = {Foley, R.D. and Suresh, S.}, title = {Stochastically Minimizing the Makespan in Flowshops}, journal = naval, year = 1984, volume = {{\bf 31}}, pages = {551--557} } @article{Fol86, author = {Foley, R.D. and Suresh, S.}, title = {Scheduling $n$ Non-Overlapping Jobs and Two Stochastic Jobs in a Flow Shop}, journal = naval, year = 1986, volume = {{\bf 33}}, pages = {123--128} } @article{Fri65, author = {Friedman, H.D.}, title = {Reduction methods for tandem queueing systems}, journal = or, year = 1965, volume = {{\bf 13}}, pages = {121--131} } @article{Gre88, author = {Greenberg, B.S. and Wolff, R.W.}, title = {Optimal order of servers for tandem queues in light traffic}, journal = ms, year = 1988, volume = {{\bf 34}}, pages = {500--508} } @article{Hil79, author = {Hillier, F.S. and Boling, R.M.}, title = {On the optimal allocation of work in symmetric balanced production line systems with variable operation times}, journal = ms, year = 1979, volume = {{\bf 25}}, pages = {721--728} } @article{Hor92b, author = {Hordijk, A. and Koole, G.}, title = {The $\mu c$-rule is not optimal in the second node of the tandem queue: a counterexample}, journal = aap, year = 1992, volume = {{\bf 24}}, pages = {234--237} } @article{Hua90, author = {Huang, C.C. and Weiss, G.}, title = {On the Optimal Order of $M$ Machines in Tandem}, journal = {Operations Research Letters}, year = 1990, volume = {{\bf 9}}, pages = {299--303} } @article{Kij89, author = {Kijima, M. and Makimoto, N. and Shirakawa, H.}, title = {Stochastic Minimization of the Makespan in Flow Shops with Identical Machines and Buffers of Arbitrary Size}, journal = or, year = 1989, volume = {{\bf 38}}, pages = {924--928} } @article{Kij90, author = {Kijima, M. and Makimoto, N.}, title = {On interchangeability for exponential single-server queues in tandem}, journal = jap, year = 1990, volume = {{\bf 27}}, pages = {459--464} } @article{Leh86, author = {Lehtonen, T.}, title = {On the Ordering of Tandem Queues with Exponential Servers}, journal = jap, year = 1986, volume = {{\bf 23}}, pages = {115--129} } @article{Mut79, author = {Muth, E.J.}, title = {The Reversibility Property of Production Lines}, journal = ms, year = 1979, volume = {{\bf 25}}, pages = {152--158} } @article{Mut84, author = {Muth, E.J.}, title = {Stochastic Processes and Their Network Representations Associated with a Production Line Queueing Model}, journal = {European J. Operations Research}, year = 1984, volume = {{\bf 15}}, pages = {63--83} } @inproceedings{Pin82f, author = {Pinedo, M.}, title = {On the optimal order of stations in tandem queues}, booktitle = {Applied Probability - Computer Science: The Interface}, year = 1982, editor = {R. Disney and T. Ott}, publisher = {Birkhauser, Boston, MA}, pages = {307--326} } @article{Pin82g, author = {Pinedo, M. and Wolff, R.W.}, title = {A Comparision Between Tandem Queues with Dependent and Independent Service Times in Tandem Queues}, journal = or, year = 1982, volume = {{\bf 30}}, pages = {464--489} } @article{Pin91, author = {McCormick, S.T. and Pinedo, M. and Shenker, S. and Wolf, B.}, title = {On the Transient Behaviour of an Assembly Line with Blocking}, journal = {International Journal of Flexible Manufacturing Systems}, year = 1991 } @article{Pin92, author = {Pinedo, M. and Shaw, D. and Chao, X.}, title = {On optimal permutation scheduling in stochastic proportionate flowshops}, journal = peis, year = 1992, volume = {{\bf 6}}, pages = {513--524} } @unpublished{Sha89, author = {Shanthikumar, J.G. and Yamazaki, G. and Sakasegawa, H.}, title = {Characterization of Optimal Order of Servers in a Tandem Queue with Blocking}, year = 1989 } @article{Tem74, author = {Tembe, S.V. and Wolff, R.W.}, title = {The optimal order of service in tandem queues}, journal = or, year = 1974, volume = {{\bf 30}}, pages = {148--162} } @article{Tso87, author = {Tsoucas, P. and Walrand, J.}, title = {On the interchangeability and stochastic ordering of {$/M/1$} queues in tandem}, journal = aap, year = 1987, volume = {{\bf 16}}, pages = {515--520} } @article{Web79, author = rrw, title = {The interchangeability of {$\cdot /M/1$} queues in series}, journal = jap, year = 1979, volume = {{\bf 16}}, pages = {690--695} } @unpublished{Web91c, author = rrw # {and Weiss, G.}, title = {The Cafeteria Process --- Tandem Queues with 0 -- 1 Dependent Service Times and the Bowl Shape Phenomenon}, year = 1991, note = {submitted for publication} } @article{Web92, author = rrw # {and Weiss, G.}, title = {Tandem queues with 0--1 service times}, journal = {in preparation}, year = 1992 } @article{Web92a, author = rrw, title = {The interchangeability of tandem queues with heterogeneous customers and dependent service times}, journal = jap # {{\rm (to appear)}}, year = 1992, pages = {to appear} } @article{Web94, author = {Weber, R.R. and Weiss, G.}, title = {The Cafeteria Process -- Tandem queues with $0$--$1$ Service Times and the Bowl Shape Phenomenon}, journal = {Operations Research}, year = 1994 } @article{Whi85, author = {Whitt, W.}, title = {The Best Order for Queues in Series}, journal = ms, year = 1985, volume = {{\bf 31}}, pages = {475--487} } @article{Wie86, author = {Wie, S.H. and Pinedo, M.L.}, title = {On the Minimization of Expected Makespan and Flowtime in Stochastic Flowshops with Blocking}, journal = mor, year = 1986, volume = {{\bf 11}}, pages = {336--342} } @article{Wol82, author = {Wolff, R.W.}, title = {Tandem Queues with dependent Service Times in Light Traffic}, journal = or, year = 1982, volume = {{\bf 30}}, pages = {601--618} }