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Mail S. Kellogg

Given a word problem, be able to develop an appropriate markov chain model.

Given a problem description, be able to write the one-step transition probability matrix.

Be able to classify the states of a markov chain given the one-step transition probability matrix.

Given an ergodic chain and the one-step transition probability matrix, be able to compute the steady state transition probabilities.

Given an ergodic chain and the one-step transition probability matrix, be able to compute multiple step transitions.

Given a simple cost function and the steady state transition probabilities, be able to compute the long run expected average costs.

- Given an M/M/1 with arrival rate lambda and service rate mu, be able to compute
- the steady state average number in the system
- the steady state average number in the queue
- the steady state average time in the system
- the steady state average wait time in the queue
- the percentage of time a server is idle.
- the steady state average number in the queue
- the percentage of time a server is idle
- the percentage of time a customer balks
- the steady state average number in the queue
- the percentage of time one or more servers is idle

Given a general queue with rate transition diagram, be able to determine the steady state probabilities,the average number in the system, and the average number in the queue.

Given a queue with finite capacity, be able to use the formulas, charts, or rate diagrams to determine

Given a queue with finite capacity, steady probabilities, and the average number in the queue/system, be able to use the revised Little's formula to determine the average number in the system/queue.

Given a queue with multiple servers, be able to use the formulas or charts to determine

Given a g(N) cost function be able to determine the minimum cost between two alternatives

~~Given an h(w) cost function be able to determine the minimum cost between two alternatives.~~

*Non-Markovian Ques, Jackson Networks*

Given a G/M/1, M/G/1, or G/G/1 queue, be able to determine performance metrics Lq and Wq.

Given an M/G/1 queue with arrival rate, service rate, and service time standard deviation, be able use the formulas to calculate Po, Lq and Wq.

Given an GI/G/1 queue with arrival rate, service rate, and service time standard deviation, be able use the formulas to calculate Po, Lq and Wq.

Given a GI/G/s queue with arrival rate, service rate, service standard deviation, and multiple servers, be able to approximate a solution for Po, Lq and Wq.

Given an M/D/1 queue with arrival rate and deterministic service time, be able to calculate Po, Lq and Wq.

Given a simple Jackson Network be able to calculate the input arrival rate for each station.

Given a simple Jackson Network with input arrival rates, be able to calculate Lq, Wq, L, W for any given station.

Given a summary table of performance metrics for a Jackson Network, be able to identify bottlenecks for the network.

*Simulation*

Given a set of parameters and an initial seed, be able to use a mixed congruential generator to generate a random number stream.

Given a random number stream and an analytic cdf, be able to use the inverse transformation method to generate random observations of a process.Given a set of interarrival and service times for a process, be able to generate the simulation event clock for a simple queuing problem.

~~Given a plot of a time varying statistic, be able to compute the statistical average; e.g., average number in queue, average number in system, ...)~~Conceptual: understand the assumptions associated with analytic models, approximate analytic models, and simulation models and when you might use a different model.

Conceptual: know the process by which to determine whether or not a queuing problem is markovian or non-markovian.