Blocking in all-optical networks

We present an analytical technique of very low complexity, using the inclusion-exclusion principle of combinatorics, for the performance evaluation of all-optical, wavelength-division multiplexed networks with no wavelength conversion. The technique is a generalized reduced-load approximation scheme which is applicable to arbitrary topologies and traffic patterns. One of the main issues in computing blocking probabilities in all-optical networks is the significant link load correlation introduced by the wavelength continuity constraint. One of the models we propose takes this into account and gives good results even under conditions with high link load correlation. Through numerous experiments we show that our models can be used to obtain fast and accurate estimates of blocking probabilities in all-optical networks and scale well with the path length and capacity of the network. We also extend one of our models to take into account alternate routing, in the form of Fixed Alternate Routing and Least Loaded Routing.

I. Introduction

Wavelength-Division multiplexing (WDM) is a promising technology which, in conjunction with wavelength routing, is making optical networks with hundreds of nodes and throughput of the order of Gbs/sec per node practical. This is because wavelength routed all- optical networks, in conjunction with WDM, offer wavelength reuse and remove the electro-optic bottleneck. In this work we consider circuit switched all-optical networks since they are a natural outcome of current WDM technology [13]. Circuit (or lightpath) requests arrive at random and are assigned a free wavelength (if available) on each link of the path they use for the duration of the request. A common metric of performance in conventional circuit-switched networks is the call blocking probability, that is, the probability that a call cannot be accepted. Telephony networks set up and tear down voice circuits over the order of minutes which makes blocking probability an important metric. In all-optical networks, lightpaths carry data at speeds of Gb/s and are set up or torn down over the order of weeks or months which is a much larger time scale. However, blocking probability can still be a reasonable metric for optical networks. This is because with growing traffic, lightpaths in the US and Europe are being leased for varying time durations. Hence, a wavelength is increasingly being viewed as a circuit. There is also a thrust by equipment vendors and service providers in developing standards such as GMPLS [3] which would enable client IP routers to request and tear down lightpaths in the optical core backbone. In this scenario, wavelengths are very similar to circuits. More importantly, the blocking model is still applicable over the order of holding times (though it now takes longer to reach steady state) and blocking probability computations can be used to dimension network and link capacities while taking into account the dynamics of lightpath requests. These observations suggest that blocking probability is still a useful metric in analysing the performance of optical networks.