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Advanced Topics in Queueing Theory and Optimization in Decision Processes

This comprehensive overview explores various optimization models and decision-making processes using Markov models and queueing theory. Key topics include probability review, inventory models, simulation projects, and practical case studies, such as diet problems, vehicle routing, and pricing strategies. The coursework incorporates theoretical foundations from utility theory and game theory, alongside applications in real-world service systems. Understanding these concepts equips students with the tools to analyze complex systems and make informed decisions in operations management.

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Advanced Topics in Queueing Theory and Optimization in Decision Processes

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  1. Previously • Optimization • Probability Review • Inventory Models • Markov Decision Processes

  2. Agenda • Hwk • Projects • Additional Topics • Finish queues • Start simulation

  3. Projects • 10% of grade • Comparing optimization algorithms • Diet problem • Vehicle routing • Safe-Ride • Limos • Airplane ticket pricing • Over time • Different fare classes / demands

  4. Additional Topics? • Case studies • Pricing options • Utility theory (ch 9-10) • Game theory (ch 16)

  5. service rate µ departures arrivals rate  queue servers c system Queues • M/M/s (arrivals / service / # servers)M=exponential dist., G=general • W = E[T], Wq = E[Tq] waiting time in system (queue) • L = E[N], Lq = E[Nq] #customers in system (queue) •  = /(cµ) utilization (fraction of time servers are busy)

  6. Networks of Queues (14.10) • Look at flow rates • Outflow =  when  < 1 • What is the distribution between arrivals? • Not independent, formulas fail. • Special case: all queues are M/M/s “Jackson Network” Lq just as if normal M/M/s queue

  7. Queueing Resources • M/M/s • Online http://www.usm.maine.edu/math/JPQ/ • Lpc(rho,c) function from textbook (fails on excel 2007,2008) • G/G/s • QTP (fails on mac excel) http://www.business.ualberta.ca/aingolfsson/QTP/ • G/G/s + Networks • Online http://staff.um.edu.mt/jskl1/simweb • ORMM book queue.xla at http://www.me.utexas.edu/~jensen/ORMM/frontpage/jensen.lib

  8. Distribution of Queue Length • Why care? • service guaranteesemergency response, missed flights • M/M/1 case • N+1 ~ Geometric(1-) • Otherwise, • ORMM add-in “state probabilities” P(N=k)

  9. ER Example (p508) Surgery c=3 µ=2/hr 12/hr 2/hr 1/6 5.3/hr 1/3 3.3/hr 5/6 Diagnosis c=4 µ=4/hr 10/hr 2/3 Other units

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