On queues with inter-arrival times proportional to service times

A family of queuing systems in which the interarrival time I/sub n+1/ between customers n and n+1 depends on the service time B/sub n/ of customer n is considered. Specifically, cases where the dependency between I/sub n+1/ and B/sub n/ is a proportionally relation and B/sub n/ is an exponentially distributed random variable is considered. Such dependencies arise in the context of packet-switched networks from employing rate policing functions which regulate the amount of data that can arrive at a link within any given time interval. The models developed and the associated solutions are, however, of independent interest and potentially applicable to other environments. Several scenarios that consist of adding an independent random variable to the interarrival time, allowing the proportionality to be random, and the combination of the two are considered. Numerical results are compared to those for an equivalent system without dependencies.<<ETX>>

[1]  Israel Cidon,et al.  Congestion control for high speed packet switched networks , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[2]  Roch Guérin,et al.  Analysis of a correlated queue in a communication system , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[3]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

[4]  Christos Langaris,et al.  Busy-period analysis of a correlated queue with exponential demand and service , 1987, Journal of Applied Probability.

[5]  Nasser Hadidi,et al.  Queues with Partial Correlation , 1981 .

[6]  Nasser Hadidi.  Further Results on Queues with Partial Correlation , 1985, Oper. Res..

[7]  J. Kingman.  Some inequalities for the queue GI/G/1 , 1962 .

[8]  O. J. Boxma,et al.  On a tandem queueing model with identical service times at both counters, I , 1979, Advances in Applied Probability.

[9]  B. W. Conolly,et al.  A Comparison of the Operational Features of Conventional Queues with a Self‐Regulating System , 1969 .

[10]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Ward Whitt,et al.  Dependence in packet queues , 1989, IEEE Trans. Commun..

[12]  B. W. Conolly,et al.  A Correlated Queue , 1969 .

[13]  Ronald W. Wolff,et al.  A new proof of finite moment conditions for GI/G/1 busy periods , 1989, Queueing Syst. Theory Appl..

[14]  O. Boxma.  On a tandem queueing model with identical service times at both counters, II , 1979, Advances in Applied Probability.

[15]  I. Cidon,et al.  Bandwidth management and congestion control in plaNET , 1991, IEEE Communications Magazine.

[16]  Debasis Mitra,et al.  Analysis and design of rate-based congestion control of high speed networks, I: stochastic fluid models, access regulation , 1991, Queueing Syst. Theory Appl..

[17]  B. W. Conolly,et al.  The Waiting Time Process for a Generalized Correlated Queue with Exponential Demand and Service , 1979 .

[18]  C. Langaris.  A CORRELATED QUEUE WITH INFINITELY MANY SERVERS , 1986 .

[19]  B. W. Conolly,et al.  The Waiting Time Process for a Certain Correlated Queue , 1968, Oper. Res..

[20]  Roch Guérin,et al.  A unified approach to bandwidth allocation and access control in fast packet-switched networks , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.