Course Objectives


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Mail S. Kellogg



Markov Chains

    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 ergodic chain and the one-step transition probability matrix, be able to compute the expected first transition times.

Queueing Theory
    Given an M/M/1 with arrival rate lambda and service rate mu, be able to compute
    1. the steady state average number in the system
    2. the steady state average number in the queue
    3. the steady state average time in the system
    4. the steady state average wait time in the queue
    5. the percentage of time a server 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
    1. the steady state average number in the queue
    2. the percentage of time a server is idle
    3. the percentage of time a customer balks

    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
    1. the steady state average number in the queue
    2. the percentage of time one or more servers is idle

    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.