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Unformatted text preview: October 6, 2004 Queueing Systems: Lecture 1 Amedeo R. Odoni Topics in Queueing Theory Introduction to Queues Littles Law Markovian BirthandDeath Queues The M/M/1 and Other Related Queues The M/G/1 Queue and Extensions Priority Queues Some Useful Bounds Congestion Pricing Queueing Networks; State Representations Dynamic Behavior of Queues 1 Lecture Outline Introduction to queueing systems Conceptual representation of queueing systems Codes for queueing models Terminology and notation Littles Law and basic relationships Reference: Chapter 4, pp. 182193 Queues Queueing theory is the branch of operations research concerned with waiting lines (delays/congestion) A queueing system consists of a user source, a queue and a service facility with one or more identical parallel servers A queueing network is a set of interconnected queueing systems Fundamental parameters of a queueing system:  Demand rate  Capacity (service rate)  Demand interarrival times  Service times  Queue capacity and discipline (finite vs. infinite; FIFO/FCFS, SIRO, LIFO, priorities) Myriad details (feedback effects, balking, jockeying, etc.) 2 C C C C C C C C C C C C C A Generic Queueing System Source of users/ customers Queue Servers Size of user source Arrivals process Queue discipline and Queue capacity Service process Number of servers Arrival point at the system Departure point from the system Queueing network consisting of In 1 5 a choice + 4 2 3 Out five queueing systems Queueing system Queueing system Point where users make Point where users merge Queueing system Queueing system Queueing system 3 Applications of Queueing Theory Some familiar queues: _ Airport checkin; aircraft in a holding pattern _ Automated Teller Machines (ATMs) _ Fast food restaurants _ Phone centers lines _ Urban intersection _ Toll booths _ Police or other spatially distributed urban services...
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 Fall '06
 hansman

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