Lecture 7: Service Times

Handouts

Syllabus (PDF)
Service Times:1. Lecture (PDF-3.9MB)2. Full version, Winter 2006 (PDF-4.6MB)
Calculating the Offered Load (from an Exam, in Hebrew) (PDF-151KB)
Haifa Municipality Example (PDF-500KB)
Phase Type Distributions (PDF-200KB)
Lecture 7: Web Summary (PDF-3.9MB)

Related Materials

Fitting Phase-Type Distributions to Data from a Telephone Call Center – M.Sc Thesis Lecture, Eva Issaev (PPT-620KB)
Service Times in Call Centers: Agent Heterogeneity and Learning with some Operational Consequences. By Gans N., Liu N., Mandelbaum A., Shen H. and Ye H. (PDF 975KB)
Modelling healthcare systems with phase-type distributions. By Mark Fackrell, Health Care Manag Sci (2009) 12:11–26 (PDF-516KB)
“On pooling in queueing networks”, Mandelbaum, A. and Reiman, M., Management Science, 44, 971-981, 1996 (PDF-180KB)
A continuous time Markov model for the length of stay of elderly people in institutional long-term care. By Xie, Chaussalet, and Millard, 2003 (PDF-170KB)
Reading Packet for Service Times:
Phase-type distributions; The queue PH/PH/1:
- Issaev, Eva: “Fitting phase-type distributions to data from a call center”, M.Sc. thesis, Technion IE\&M, 2003. (With sample references and a literature review.) http://iew3.technion.ac.il/serveng/References/Thesis.pdf
- Neuts, M.F., Matrix Geometric Solutions in Stochastic Models, John Hopkins University Press, 1981.
- Asmussen Soren, Nerman Olle and Olsson Marita,
  1. “Fitting phase type distributions via the EM algorithm”. Preprint, Goteborg Univ., 1994.
  2. EMPHT-A program for fitting phase-type distributions. Preprint, 1992.
- Kang, Sungyeol and Serfozo, Richard, F., “Parallel-processing times: extreme values of phase-type and mixed random variables”, preprint, 1995.
- Bitran, G.R. and Dasu, S., “Analysis of the ΣPHi/PH/1 queue”, Operations Research, 42, 158-174, 1994.
- Buzacott, John A. and Shanthikumar, George J., Stochastic Models of Manufacturing Systems, Prentice-Hall, 1993. Chapter 3, pages 43–97, “Single-stage `Produce-to-order’ Systems”. Not easy reading: analysis of waiting times; PH/PH/1 (3.3.3); G/G/C approximations (3.4.2).

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