Reading for Fluid Models

Optional Packet: Fluid Models

• Hall, Chapter 6.
  Relevant here: Section 6.4, pages 186–199, on Short Service Times, Sec.6.5, on long service-times;  Sec.6.7, on Queueing to Meet a Schedule (better in Newell, Sec.2.5?).

• R.W. Hall, Transportation Queueing (a review chapter on Queueing Theory) in Handbook of Transportation Science, 2nd Edition, R.W. Hall editor, Kluwer Scientific Publishers, Norwell, Massachusetts, 2002, Pages  113-153.

• Newell, G.F., Applications of Queueing Theory,
  Prefaces to the 1st and 2nd Edition;
  Chapter 1, Introduction;
  Chapter 2, on “Deterministic Fluid approximations – single server”.

Optional Packet: Fluid Models -Applications

• Oliver, R.M. and Samuel, A.H., “Reducing letter delays in post offices”. Operations Research, 10, 839–892, 1962.
  (An early classic application of the Fluid-approach.)

• Vandergraft, James S., “A fluid model of networks of queues”, Management Science, 29, 1198–1208.
  (Fluid models, without boundary constraints, namely in the overloaded region. Applied to Administrative Queues, which is here claims processing in a Social Security Administration District Office.)

• National Cranberry Cooperative: a well-known Harvard case, published and analyzed in Interfaces, through 3 articles, edited by Evan Porteus, as follows:

1. 1. “The case analysis section: National Cranberry cooperative”, 19, 29–39, 1989.
   2. “Analysis of tactical options”, 23, 21–39, 1993.
   3. “Environmental changes and implementation”, 23, 81–92, 1993.

• D. C. Schmidt, D. A. Hoe in and R. A. Skoog,  “Simple Models of Complex Transient Phenomena”, Teletraffic Contributions for the Information Age, Proceedings of ITC 15, V. Ramaswami and P. W. Wirth (eds.), Elsevier, Amsterdam, 1997, pp. 953-964.
• Massey, W.A., W.Whitt. “Peak Congestion in Multi-Server Systems with Slowly Varying Arrival Rates”, Queueing Systems, 25 (1997), pp. 157–172.
• Tosic, Vojin, “A review of airport passenger terminal operations analysis and modelling”, Transportation Research A, 26A, 3–26, 1992. (Limited to terminal building from the entrance/exit at the landside to the gates, i.e., it does not include airport access. See Figure 1, for an S-shaped arrival curve.)

• Koopman, Bernard, O., “Air-terminal queues under time-dependent conditions”, Operations Research, 20, 1089–1114, 1972.
  (Analysis and applications of M_t/G/S/N(G =M or D), with comparison to Fluid models, as described on pages 1098–1099.)

• Hall, R.W., “Graphical models for manpower planning”, Int. J. Production Research, 24, 1267–1282, 1986. (Normative aggregate models, that highlight and clarify fundamental cost tradeoffs, otherwise obscured; presented through graphs and figures, rather than algebraic expressions.)

Optional Packet: Fluid Models -Theory

• Harrison, J.M., Brownian Motion and Stochastic Flow Systems, Wiley, 1985. (Chapter 2 presents fluid models,“our way”.)

• El-Taha, Muhammad and Stidham, Shaler, “Sample-Path Analysis of Queueing Systems”, Kluwer, 1999. (A deterministic (sample-path) approach for analyzing stochastic systems, primarily queueing systems and more general input-output models.)

• Dai, Jim G., “Stability of open multiclass queueing networks via Fluid models”, in Stochastic Networks, editors Kelly and Williams, pages 71–90. (The modern approach to establishing stability; see the Appendix to your Homework on “Capacity Analysis and Little’s Law”.)
  Downloadable from: https://www2.isye.gatech.edu/~dai/publications/dai95b.pdf

• Dai, Jim. G., “A fluid-model criterion for instability of multiclass queueing networks”. Preprint, 7 pages, 1996.

• Banks J. and Dai J.G., ”Simulation studies of multiclass queueing networks”, IIE Transactions, Vol 29,213-219 (1997).

Downloadable from: https://link.springer.com/article/10.1023/A:1018519112134

Optional Packet: Fluid Models -personal involvement

• QED Q’s: Eurandom 2003 Tutorial, Part C on Predictable Queues and Fluid Models. (Downloadable in our website)

• Chen, Hong and Mandelbaum, A., “Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations”, Math. of Operations Research, 16, 408–446, 1991.
  (A basic network model; the traffic equations.)

• Chen, Hong, and Mandelbaum, A., “Hierarchical modeling of stochastic networks, Part 1: Fluid models”. In Stochastic Modeling and Analysis of Manufacturing Systems, Yao D., Editor, pages 47–105, Springer-Verlag, 1995.
• Mandelbaum, A. and Massey, William, A., “Strong approximations for time-dependent queues”, Math. of Operations Research,20,33–64, 1995.
• Mandelbaum, A. and Pats, Gennady,  “State-dependent stochastic networks. Part 1: Approximations and applications with continuous diffusion limits”, The Annals of Appl. Prob., 8, 569-646, 1998.
• 3-Part series, with collegaues at Bell-Labs (Massey, W.A., Reiman,M., Stolyar,A.) and with Rider, B. (was a post-doc at Technion) , on “Queue Lengths and Waiting Times for Multiserver Queues with Abandonment and Retrials”, 1998-2000. Downloadable in our website:
  1. M.,Massey, Reiman, Rider: “Time Varying Multi-server Queues with Abandonment and Retrials”, ITC-16, 1999.
  2. M.,Massey, Reiman, Rider and Stolyar: “Waiting Time Asymptotics for Time Varying Multiserver Queues with Abandonment and Retrials”, Allerton Conference, 1999.
  3. M.,Massey, Reiman, Rider and Stolyar: “Queue Lengths and Waiting Times for Multiserver Queues with Abandonment and Retrials”, Fifth INFORMS Telecommunications Conference, 2000.