1. Background on Relevant Stochastic Processes [e.g., Green Ross (2010), Blue Ross (1996) and Asmussen (2003), ordered in increasing difficulty]

   • Poisson process, renewal theory, Markov chains, diffusion processes, stationary marked point processes

2. Little's Law and Fundamental Conservation Laws [Wolff (1989), El-Taha and Stidham (1999)]

   • A Review of L = W and Extensions. 1991 review paper.

3. Markovian Queueing Models [Green Ross, Secs. 8.3 & 8.4, Cooper (1982), Wolff (1989)]
   • Birth-and-Death Models [Green Ross Chs 5 & 6, Sec. 6.3; Blue Ross, Ch.5, Asmussen, Chs. II-IV]
     • M/M/1

     • Infinite-Server: M/M/infinity

     • Erlang C (delay, M/M/s/infinity), B (loss, M/M/s/0) and A (with abandonments, M/M/s+M), M/M/s/r, general BD

       • More to know about Erlang models and general BD processes:

         • The Erlang B and C Formulas: Problems and Solutions. properties and computation.

         • Transient behavior of BD processes: J. Keilson, Markov Chain Models-Rarity and Exponentiality, Springer, 1979.

         • Calculating Transient Characteristics of the Erlang Loss Model by Numerical Transform Inversion.

         • Computing Laplace Transforms for Numerical Inversion Via Continued Fractions. How to calculate first-passage time distributions in general birth-and-death processes, exploiting continued fractions.

   • Reversibility and Queueing Networks [Kelly (1979)]
     • open networks

     • closed networks

     • loss networks
       • Blocking When Service is Required from Several Facilities Simultaneously. The Erlang fixed point approximation. See extensive related work by F. Kelly.

4. Single-Server Queues Beyond M/M/1 (or Queues with Few Servers, FCFS reference case)
   • classical M/G/1, Pollaczek-Khintchine theory. [Blue Ross, Ex. 4.3a]

   • G/G/1 [Asmussen, Chs. 8 & 10.]
     • Matrix analytic theory [books by Neuts, Asmussen, Ch. XI]

     • numerical transform inversion

       • Numerical Inversion of Laplace Transforms of Probability Distributions. short 1995 paper, good place to start.

       • The Fourier-Series Method for Inverting Transforms of Probability Distributions. long 1992 paper. applications to M/G/1.

       • Calculation of the GI/G/1 steady-State Waiting-Time Distribution and its Cumulants from Pollaczek's Formula. calculates steady-state distribution for general GI/GI/1 queue.

     • Heavy-traffic theory

       • Stochastic-Process Limits. WW's 2002 book, Chs. 5 & 9 after basics in Chs. 1-4.

       • J. M. Harrison, Brownian Motion and Stochastic Flow Systems, 1985.

     • Non-FCFS Service Disciplines
       • priority queues [Wolff Ch. 10]

       • processor-sharing (PS), shortest-remaining processing time (SRPT, etc.

     • Networks of G/G/1 Queues [WW 2002 book, Ch. 14, WW 1983 QNA paper]
       • The Queueing Network Analyzer., 1983 paper on parametric-decomposition approximation method.

       • Personal bibliography on approximations for queueing networks.

       • Stochastic-Process Limits. heavy-traffic approximations, WW's 2002 book, Ch. 14.

5. Many-Server Queues
   • Infinite-Server Queues, Offered-Load Analysis

   • Many-Server Loss Models

   • Many-Server Delay Models, Possibly with Customer Abandonment

     • Heavy-Traffic Theory

       • Understanding the Efficiency of Multi-Server Service Systems. WW 1992 paper.

         Martingale Proofs of Many-Server Heavy-Traffic Limits for Markovian Queues. 2007 Survey paper by Guodong Pang, Rishi Talreja and WW.

         Fluid Models for Multiserver Queues with Abandonments. WW 2006 paper.

     • Parallel Service Systems, Skill-Based Routing

       • A Staffing Algorithm for Call Centers with Skill-Based Routing. 2005 paper by Rodney Wallace from IBM and WW.

       • Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems. 2009 paper by Itai Gurvich and WW.

       • An ODE for an Overloaded X Model Involving a Stochastic Averaging Principle. 2011 paper by Ohad Perry and WW.

6. Time-Varying Arrival Rates
   • Many-Server Queues with Time-varying Arrival Rates
     • Coping with Time-Varying Demand when Setting Staffing Requirements for a Service System. 2007 survey paper by Linda Green, Peter Kolesar and WW.

     • What You Should Know About Queueing Models to Set Staffing Requirements in Service Systems. short review paper by WW.

     • Dynamic optimization with applications, 2010 INFORMS tutorial paper by Robert Hampshire and Bill Massey.

     • The Erlang-R Queue: Time-Varying QED Queues with ReEntrant Customers in Support of Healthcare Staffing�. by Avishai Mandelbaum and GY. Submitted to Manufacturing and Service Operations Management.

     • The G_t/GI/s_t+GI Many-Server Fluid Queue. paper by Yunan Liu and WW.

     • Many-Server Heavy-Traffic Limits for Queues with Time-Varying Parameters. 2011 paper by Yunan Liu and WW.