Queuing Systems: Lecture 1 Amedeo odoni October 10. 2001
Queuing Systems: Lecture 1 Amedeo R. Odoni October 10, 2001
Topics in Queuing Theory 9. Introduction to Queues: Little' s law: M/M/ 10. Markovian Birth-and-Death Queues 11. The M/G/1 Queue and Extensions 12. Priority Queues; State Representations 13. Congestion Pricing 14. Dynamic Behavior of Queues 15. Hypercube Queuing Model 16. The Queue Inference Engine; Psychology of Queues
Topics in Queuing Theory 9. Introduction to Queues; Little’s Law; M/M/1 10. Markovian Birth-and-Death Queues 11. The M/G/1 Queue and Extensions 12. Priority Queues; State Representations 13. Congestion Pricing 14. Dynamic Behavior of Queues 15. Hypercube Queuing Model 16. The Queue Inference Engine; Psychology of Queues
Lecture outline Introduction to queuing systems Conceptual representation of queuing systems Codes for queuing models Terminology and notation Little's Law and basic relationships Birth-and-death processes The M/M/1 queuing system State transition diagrams Steady-state probabilities
Lecture Outline • Introduction to queuing systems • Conceptual representation of queuing systems • Codes for queuing models • Terminology and notation • Little’s Law and basic relationships • Birth-and-death processes • The M/M/1 queuing system • State transition diagrams • Steady-state probabilities
Queues Queuing Theory is the branch of operations research concerned with waiting lines (delays/congestion A queuing system consists of a user source, a queue and a service facility with one or more identical parallel servers a queuing network is a set of interconnected queuing systems Fundamental parameters of a queuing system Demand rate Capacity(service rate Demand inter-arrival times Service times Queue capacity and discipline(finite VS infinite FIFO/FCFS, SIRO, LIFO, priorities) Myriad details(feedback effects, jockeying", etc.)
Queues • Queuing Theory is the branch of operations research concerned with waiting lines (delays/congestion) • A queuing system consists of a user source, a queue and a service facility with one or more identical parallel servers • A queuing network is a set of interconnected queuing systems • Fundamental parameters of a queuing system: Demand rate Capacity (service rate) Demand inter-arrival times Service times Queue capacity and discipline (finite vs. infinite; FIFO/FCFS, SIRO, LIFO, priorities) Myriad details (feedback effects, “jockeying”, etc.)
A Generic Queuing System servers Arrival point C Departure point at the system from the system C Qu ueue Source ofusers/ CCCCCC C customers CCc Arrivals rocess pre Size of Queue discipline and Service process Number of servers user source Queue capacity
A Generic Queuing System Source of users/ customers C C C C C C Queue C C C C C C C 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