1999
DOI: 10.1049/el:19991500
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Waiting time distribution in M/D/1 queueing systems

Abstract: Abstrzict ' Elenientary congestion models sornetimes require analysis of G/Gfl systems with hyperexponentially distributed interarrival time and service time distributions. It is shown that for such systems, the ergodic waiting time distribution is itself hyperexponentially distributed, A siinple computational procedure is provided to find the parameters needed, Green's function methods are employed to motivate the factorization required, The releyance of these results to the delay in the overflow process of M… Show more

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Cited by 26 publications
(17 citation statements)
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“…By the PASTA property [15], the amount of unprocessed work U 1 (x) is identical to the waiting time of a customer when service is first-come, first-served. The waiting time distribution W 1 (x) in a M/D/1 system can be written as [16]: where q is the largest integer less than or equal to x, q = bxc. Finally P L is:…”
Section: Queue Modelmentioning
confidence: 99%
“…By the PASTA property [15], the amount of unprocessed work U 1 (x) is identical to the waiting time of a customer when service is first-come, first-served. The waiting time distribution W 1 (x) in a M/D/1 system can be written as [16]: where q is the largest integer less than or equal to x, q = bxc. Finally P L is:…”
Section: Queue Modelmentioning
confidence: 99%
“…In particular, for the Exponential distribution of the packet interarrival times, we apply the M/D/1 steady-state analysis [34] to express probability p that the queuing delay experienced by a packet exceeds Q packets:…”
Section: B Target Utilization Belowmentioning
confidence: 99%
“…Proof: This is a straightforward derivation of classical queuing theory. A numerical method to solve the equation can be found in [14] Combined with Equation 2, we can thus obtain the probability of packet loss as a function of N 6 , τ, and λ.…”
Section: A One Interface Sipnatmentioning
confidence: 99%