Office Hours: TBA (and by appointment), Room 325, Schreiber (Mathematics) Building
+972-3-640-9637.
Fall semester 2011: Tuesday 15:00 - 18:00
9:00 am, February 6, 2012
Probability Theory, Operations Research 1 (or equivalent), Introd. to Stochastic Processes (or equivalent)
Queueing Theory deals with the analysis and design 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 servers to become available, the customers form 'waiting lines', or queues.
Queueing theory is extensively applied in various areas, including Communication and Computer Networks, Service Systems, Manufacturing, Road Traffic Analysis, Maintenance and Reliability, etc.
Queueing theory started 102 years ago with the pioneering work of the Danish Scientist, Agner Krarup Erlang (born on January 1st, 1878), who published his paper, "The theory of probabilities and telephone conversations" (Nyt Tidsskrift for Matematik B, Vol. 20, 1909).
The course is directed to Graduate and 3rd year Undergraduate students with solid background in Probability Theory and some knowledge in Stochastic Processes.
Clasification of queueing systems; The Poisson process; Exponential and Erlang (Gamma) probability distribution functions; Laplace- Stieltjes Transforms (LSTs); Probability Generating Functions (PGFs); Order Statistics; The M/G/infinity queue.
Discrete-time model; Embedded Markov chain; The Stationary distribution and its PGF; PASTA; Khinchine-Pollaczek formula; Waiting times; Little's Law; The Busy Period and its LST; Delay Busy Period; Vacation models; Polling Systems (if time permits).
The M/M/1 and M/M/c systems; Limited Buffer systems and Erlang's Loss formula; Multi-dimensional systems.
Jackson networks; Applications to Communication Systems.
The G/M/1 and G/M/c queues; G/Ek/1; M/D/c.
Head-of-the-Line and Pre-emptive disciplines; The c-mue rule; Last-come first-served (LCFS) versus First-come first served (FCFS); Random Order of Service (ROS); Processor Sharing; Shortest Remaining Processing Time (SRPT); Right-of-Way policy.