The M/G/1 Queue

Randolph Nelson
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Randolph Nelson: OTA Limited Partnership

Chapter 7 in Probability, Stochastic Processes, and Queueing Theory, 1995, pp 283-327 from Springer

Abstract: Abstract In this chapter we analyze a simple single server queue that is frequently used to model components of computer systems. This queue is termed the M/G/1 queue. This is standard “queueing notation,” first introduced by Kendall. Typically a queue is described by four variables % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaGaa8xqai % aa-9cacaWFtbGaa83laGqaciaa+TgacaWFVaGaa43yaiaa+Xcaaaa!3C21! $$ A/S/k/c, $$ which have the following interpretation: A,S — The arrival (A) or service (S) process where M means Poisson arrivals and exponential service times, G means the process is generally distributed, E ℓ denotes an ℓ-stage Erlang distribution, and D denotes a deterministic distribution. k — The number of servers. c — The buffer size of the system. This is the total number of customers the system can hold. Arrivals to the system already containing c customers are assumed to be lost. If not specified, c is assumed to be infinite.

Keywords: Service Time; Queue Length; Busy Period; Probability Generate Function; Poisson Arrival (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4757-2426-4_7

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