DocumentCode
745845
Title
Proof of a Conjecture on the Interarrival-Time Distribution in an M/M/1 Queue with Feedback
Author
Burke, P.J.
Author_Institution
Bell Labs., Holmdel, NJ
Volume
24
Issue
5
fYear
1976
fDate
5/1/1976 12:00:00 AM
Firstpage
575
Lastpage
576
Abstract
In a Jackson-type queuing network with feedback, the equilibrium state distribution of each queue is that of an 
system. In support of a previous conjecture that nevertheless the input processes in such a network are not Poisson, the marginal interarrival-time distribution for an equilibrium 
queuing system with feedback, counting both fed-back and exogenous customers as arrivals, is calculated. Since this distribution is a mixture of two exponentials, the total input to such a system is not Poisson.
system. In support of a previous conjecture that nevertheless the input processes in such a network are not Poisson, the marginal interarrival-time distribution for an equilibrium queuing system with feedback, counting both fed-back and exogenous customers as arrivals, is calculated. Since this distribution is a mixture of two exponentials, the total input to such a system is not Poisson.Keywords
Feedback communication; Queued communications; Communication channels; Communication systems; Digital communication; Dispersion; Estimation theory; Fading; Frequency diversity; State feedback; Stochastic processes; Traffic control;
fLanguage
English
Journal_Title
Communications, IEEE Transactions on
Publisher
ieee
ISSN
0090-6778
Type
jour
DOI
10.1109/TCOM.1976.1093335
Filename
1093335
Link To Document