Queueing models of optical delay lines in synchronous and asynchronous optical packet-switching networks

Xiaoming Zhu Joseph M. Kahn University of California Department of Electrical Engineering and Computer Sciences 307 Cory Hall Berkeley, California 94720-1772 E-mail: [email protected] Abstract. Buffering with optical delay lines (ODLs) in optical packetswitching networks is a way to mitigate network contention. We study queueing models of ODLs in synchronous and asynchronous optical packet-switching networks under uniform Bernoulli traffic. We first introduce a Markov chain model for a finite-length ODL forward-buffering system in synchronized networks and calculate the stationary distribution of its queueing length as well as two important queueing parameters: packet loss rate (PLR) and average queueing delay (AQD). We then introduce an asymptotic analysis based on the generating function of an infinite buffering system and present approximate expressions for PLR and AQD. Numerical calculations demonstrate that these asymptotic estimates of PLR and AQD are quite accurate. We then extend the queueing analysis to feedback-buffering ODLs in synchronized networks. We present numerical calculations of PLRs and AQDs for feedback-buffering ODLs. Finally, we introduce queueing models in asynchronous networks for forward buffering or for feedback buffering without multiple recirculations. We carry out the asymptotic analysis to characterize the performance degradation of ODL buffering in asynchronous switching when the traffic load is high. © 2003 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.1572500]