Office Hours: Sunday 11-12, Schreiber 326
Spring semester 1999
Tuesday 16:00-19:00, Wolfson 238
Probability Theory, Operations Research 1 (or an equivalent), Introd. to Stochastic Processes (desired)
The course focuses on Stochastic methods, primarily Queueing and Reliability models, which are applicable to Industrial Engineers.
Queueing Theory deals with the analysis, design and optimization of complex systems where several 'servers' serve randomly-arriving 'customers' (e.g. jobs, calls, messages), each requiring service of random-duration length. While waiting for server(s) to become available, the customers form 'waiting lines', or queues.
Queueing theory is extensively applied in various areas, including Manufacturing, Communication and Computer Networks, Road Traffic Analysis, etc.
Reliability of a system is its probability of functioning properly for a given period of time.
Reliability theory deals with the probabilistic analysis of multi-component complex systems where the life-time of each component is random. Characterizations of such systems and their properties will be discussed in this part of the course.
The course is directed to graduate Industrial Engineers with background in Probability Theory and some knowledge in Stochastic Processes.
Probability distribution functions (Bernoulli, Geometric, Binomial, Poisson, Exponential, Erlang (Gamma), Phase-type, etc.
Generating functions, Laplace transforms
Discrete-time model (Geom/Geom/1); Continuous time formulation (Embedded Markov chain); Stationary distribution; Khintchine-Pollaczek formula; Burke's theorem; PASTA; Waiting times; Little's law; Busy period, Delay Busy Period
The M/M/1 and M/M/c queues
Truncated Models; Erlang's Loss Formula (The Parking Lot Problem); Repairman Problem (Machine interference)
Multi-Dimensional Birth and Death Processes
Applications to Computer and Communication Networks
Structure and coherent functions
Systems in Seies, Parallel and k-out-of-n
Paths and Cuts
Failure-rate and Hazard functions
IFR and DFR functions
Design and Optimization
Maintenance and Replacement