Queuing Theory By: Brian Murphy.

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Presentation transcript:

Queuing Theory By: Brian Murphy

Overview Queuing Theory: the mathematical study and analysis of waiting lines (queues). Performance Measures Involved: Arrival Rate = λ (measured in persons per unit of time) Service Rate = μ (measured in persons per unit of time) Throughput = 1/ λ (rate of successful services) Utilization = ρ = λ/ μ (portion of time a server is servicing a customer) Number of people in the system = L System Response Time = W (average time customer spends in system)

Characterizing Queues A/B/C/N/K A denotes type of arrival process B denotes type of service process C denotes number of servers N denotes system capacity K denotes customer population Types of arrival and service processes M: exponential distribution G: general distribution D: deterministic distribution E: Erlang distribution H: hyperexponential distribution Generally used because of its “memoryless” property

Common Queue: M/M/1 M/M/1 Queue: exponential arrival and service process, one server Formulas Involved: L = ρ/(1- ρ) W = (1/μ) /(1- ρ)