Abstract
We consider a retrial queueing model with collision arising from the specific communication protocolCSMAICD. Under the retrial control policy in which the retrial rate is inversely proportional to the number of customers in the retrial group, we derive the generating function of the limiting distribution of the number of customers in the retrial group at the moment when the channel is free. Using the theory of Markov regenerative processes, we also obtain the limiting distribution of the number of customers in the system at arbitrary time points.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Bertsekas and R. Gallager,Data Networks (Prentice-Hall, 1987).
B.D. Choi and K.K. Park,M/G/1 retrial queue with Bernoulli schedule, Queueing Systems 7(1990)219–228.
B.D. Choi and K.K. Park,M/G/1 retrial queue with retrial time depending on queue size, Preprint.
G. Falin, Retrial queues, Queueing Systems 7(1990)127–168.
K. Farahmand, Single line queue with repeated demands, Queueing Systems 6(1990)223–228.
G. Fayolle, E. Gelenbe and J. Labetoulle, Stability and optimal control of the packet switching broadcast channel, J. ACM 24(1977)375–386.
J.L. Hammond and P.J.P. O'Reilly,Performance Analysis of Local Computer Networks (Addison-Wesley, 1986).
D.P. Heyman, The effects of random message sizes on the performance of theCSMA/CD protocol, IEEE Trans. Commun. COM-34(1986)547–553.
V.G. Kulkarni and B.D. Choi, Retrial queue with server subject to breakdowns and repairs, Queueing Systems 7(1990)191–208.
S.S. Lam and L. Kleinlock, Packet switching in a multi access broadcast channel: Dynamic control procedures, IEEE Trans. Commun. CIM-23(1975)891–904.
J.S. Meditch and C.T.A. Lea, Stability and optimization of theCSMS andCSMA/CD channels, IEEE Trans. Commun. COM-31(1983)763–774.
N.B. Meisner, J.L. Segal and M.Y. Tanigawa, An adaptive retransmission technique for use in a slottedALOHA channel, IEEE Trans. Commun. COM-31(1983)763–774.
A.G. Pakes, Some conditions for ergodicity and recurrence of Markov chains, Oper. Res. 17(1969) 1058–1061.
F.A. Tobagi and V.B. Hunt, Performance analysis of carrier sense multiple access with collision detection, Comp. Networks 4(1980)245–259.
F.A. Tobagi and L. Kleinrock, Packet switching in radio channels, Part I: Carrier sense multiple-access mode and their throughput-delay characteristics, IEEE Trans. Commun. COM-23(1975)1400–1416.
T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2(1987)201–233.
Author information
Authors and Affiliations
Additional information
This paper was supported in part by the Non-Directed Research Fund, Korea Research Foundation, 1990.
Rights and permissions
About this article
Cite this article
Choi, B.D., Shin, Y.W. & Ahn, W.C. Retrial queues with collision arising from unslottedCSMA/CD protocol. Queueing Syst 11, 335–356 (1992). https://doi.org/10.1007/BF01163860
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01163860