Analytical Loss Models for MAC protocols in Optical Ring Network Operating under a Static Traffic Load

In this paper we analyse previously proposed MAC protocols for optical ring networks under static traffic conditions. The analytical models are developed for random order and round-robin transmission policies in both slotted and unslotted cases. The models predict the receiver efficiency, i.e. the fraction of time each receiver is active. The models are also verified by numerical simulations and some remarks are made for improving the performance of the protocols. INTRODUCTION Optical ring network is a viable solution for metropolitan area networks (MAN). In such a network optical bursts can be used to transfer the data [1, 2]. Optical burst switching (OBS) has been proposed both for regular (e.g. ring) networks as well as general mesh networks. An optical burst consists of several concatenated packets and can be seen as an intermediate step from the wavelength routed networks (i.e. circuit switching) towards the optical packet switching. Generally in OBS the source node first sends a control packet or frame to inform the receiver (and possibly intermediate nodes) about the upcoming burst. The burst is then sent after a certain offset time without waiting for any acknowledgment from the receiver (or intermediate nodes). In this paper we will consider OBS in a ring topology. In [3, 4] Xu et al. have studied a cost effective single fibre unidirectional OBS ring network, where each node has a dedicated fixed home wavelength channel for transmitting its bursts. In addition to data channels a shared control channel is used to inform the other nodes about the arriving bursts. Thus, the number of wavelength channels W is equal to N +1, where N is the number of nodes. Furthermore each node has only one adjustable receiver. Consequently, no transmissions collide in the fibre, but as each node can listen to at most one channel at a time burst losses may occur at the receiver. In [3, 4] several MAC protocols have been evaluated by numerical simulations. In all cases a round-robin transmission policy is used, i.e. each node maintains one transmission queue for each destination node and those transmission queues which have enough packets to form at least a minimum size burst are served in round-robin fashion. In this paper we study similar MAC protocols as proposed in [3, 4] under static traffic conditions. In particular, we consider both random order and round-robin transmission policies. When a node operates in random order policy the transmission queue to be served next is chosen randomly among the non-empty queues. In the analysis we consider an arbitrary receiver and derive formulae for the burst blocking probability and the so-called (receiver) efficiency γ, i.e. the proportion of the time the receiver is active. Note that in the ideal case the blocking probability is zero and the efficiency γ is equal to the offered load ρ A special attention is given to the performance under an extremely heavy load where each source has always bursts to be sent to all N −1 other destinations, i.e. the offered load is ρ = 1. Although this symmetric heavy traffic scenario does not hopefully exist, it gives us a lower bound on blocking probability for each MAC protocol and allows us to compare their worst case performance. Note that in an ideal case the blocking probability is zero and each receiver is busy all the time, leading to an average pairwise throughput of 1/(N −1) times the capacity of one channel. However, it will be shown that without any coordination between the nodes the actual throughput will be considerably less, i.e. about a half of that. The rest of the paper is organized as follows. In the next two sections an analytical models are developed for a unslotted protocol operating in both random order and round-robin order transmission policies and for a slotted protocol with random order transmission policy. Then we present some numerical examples, which verify the derived analytical results. In the fifth section some improvements to the protocols are proposed, and the last section contains the conclusions. UNSLOTTED PROTOCOL VERSION First we consider an idealized protocol model, where transmissions of each node are independent of others. In particular, the nodes can transmit bursts at any point of time, i.e. the system is unslotted [5]. Without a loss of generality, we can consider the receiver at node 0. We assume a (quasi) static scenario where, during a some reasonably long time interval, there are K nodes sending bursts to node 0. Furthermore, each node j sends bursts to a j −1 other nodes, i.e. a j denotes the number of destinations channel j source has. During this receiver 1 idle time for 2 2 2 2