This Article 
 Bibliographic References 
 Add to: 
Performance Evaluation of the Time-Stamp Ordering Algorithm in a Distributed Database
June 1993 (vol. 4 no. 6)
pp. 668-676

Time-stamp ordering is one of the consistency preserving algorithms that is used indistributed databases. F. Baccelli (1987) has introduced a queueing model thatincorporates the fork-join and resequencing synchronization constraints to analyze thealgorithm's performance. The power of interpolation approximation technique is illustrated by obtaining extremely good approximations for this rather complex model. The heavy traffic approximations are obtained by showing that this model has the same diffusion limit as a system of parallel fork-join queues. The light traffic limits are obtained by applying the light traffic theory developed by M.I. Reiman and B. Simon (1989). The heavy traffic limits are computed for general arrival and service distributions, but the light traffic limits are restricted to Markovian systems.

[1] F. Baccelli, "A queueing model for timestamp ordering in a distributed system," inPerformance '87, Brussels, 1987, pp. 413-431.
[2] F. Baccelli and A. Makowski, "Queueing models for systems with synchronization constraints,"Proc. IEEE, vol. 77, pp. 138-162, Jan. 1989.
[3] F. Baccelli and Ph. Robert, "Analysis of update response times in a distributed data base maintained by the time stamp ordering algorithm," inPerformance'83, 1983.
[4] P. Bernstein and N. Goodman, "Concurrency Control in Distributed Database Systems,"ACM Computing Surveys, Vol. 13, No. 2, June 1981, pp. 185-221.
[5] P. Billingsley,Convergence of Probability Measures. New York: Wiley, 1968.
[6] J. M. Harrison and R. J. Williams, "Brownian models of queueing networks with homogeneous customer population,"Stochastics, vol. 22, pp. 77-115, 1987.
[7] E. Kyprianou, "The virtual waiting time of theGI/G/1 queue in heavy traffic,"Adv. Appl. Prob., no. 3, pp. 249-268, 1971.
[8] R. Nelson and A. N. Tantawi, "Approximate analysis of fork-join synchronization in parallel queues,"IEEE Trans. Comput., vol. 37, no. 6, pp. 739-743, 1988.
[9] V. Nguyen, "Heavy traffic analysis of processing networks with parallel and sequential tasks," Ph.D. dissertation, Dep. Oper. Res., Stanford Univ., 1990.
[10] Y. Prohorov, "Convergence of random processes and limit theorems of probability theory,"Theor. Probability Appl., vol. 1, pp. 157-214, 1956.
[11] M. I. Reiman, "Open queueing networks in heavy traffic,"Maths. of Oper. Res., vol. 9, no. 3, pp. 441-458, 1984.
[12] M. I. Reiman and E. G. Coffman, "Diffusion approximations for computer communication systems,"Mathematical Computer Performance and Reliability, G. Iazeolla, P. J. Courtois, and A. Hordijk, Eds. Amsterdam: North Holland, 1984.
[13] M. I. Reiman and B. Simon, "Open queueing systems in light traffic,"Maths. of Oper. Res., vol. 14, no. 1, pp. 26-59, 1989.
[14] S. Varma, "Heavy and light traffic approximations for queues with synchronization constraints," Ph.D. dissertation, Univ. Maryland, 1990.
[15] S. Varma and A. M. Makowski, "Interpolation approximations for forkjoin queues" in preparation, 1992.
[16] D. Iglehart and W. Whitt, "Multiple channel queues in heavy traffic. I,"Adv. Appl. Prob., pp. 150-177, 1970.

Index Terms:
Index Termstime-stamp ordering; distributed database; consistency preserving; queueing model;fork-join; resequencing; interpolation; light traffic; database theory; distributeddatabases; interpolation; queueing theory
S. Varma, "Performance Evaluation of the Time-Stamp Ordering Algorithm in a Distributed Database," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 6, pp. 668-676, June 1993, doi:10.1109/71.242156
Usage of this product signifies your acceptance of the Terms of Use.