A Markov chain model for an optical shared-memory packet switch

A Surjective-Mapping Based Model for Optical Shared-Buffer Cross-Connect

“…Finally, the destinations of packets arriving at the secondary inputs in a given time slot are assumed to be independent of packets arriving at both primary and secondary inputs in the previous time slots. Since packet arrivals at primary inputs are assumed to be independent of each other, the number of packet arrivals at the primary inputs in a given time slot follows the binomial distribution, i.e., (1) Let be the random variable representing the total number of packets arriving at both primary and secondary inputs, i.e., (2) The packet arrivals during a given time slot at the primary inputs, represented by , are assumed to be independent of the packet arrivals during the previous time slot, on which the random variable depends. Therefore, the distribution of is given by (3) Note that…”

“…A shared-buffer switching architecture similar to that presented in Fig. 1 is analyzed based on a Reduced Markov Chain (RMC) in [1]. This RMC model significantly reduces the number of states compared to that of Full Markov Chain (FMC) based model previously developed to study similar architectures [20].…”

“…The switch is augmented with FDLs. Each fiber line can either be passive or augmented with an amplifier [1]. The inputs to the switch from the FDLs will be referred to as secondary inputs.…”

“…The propagation time delay is usually chosen to be a multiple of the packet transmission time. Optical buffering schemes that use FDL for contention resolution can be divided into two categories: feedforward [9], [11], [14], [15], and feedback FDL buffering [1], [3], [12], [17]. In feed-forward buffering, a contending packet is delayed at the output port and leaves the node after the propagation delay of the traversed FDL.…”

“…Therefore, a shared-FDL cannot be analyzed as an isolated module due to the interdependency among arrivals from different input ports to the switch [1]. Nevertheless, feedback architecture achieves better performance in terms of the packet loss rate than that achievable through a comparable feed-forward architecture [16].…”