An Analytical Model for a Book-Ahead Bandwidth Scheduler

Optical networks with book-ahead bandwidth schedulers are being deployed to meet the high-speed and predictable-service networking requirements of applications in the scientific research community. We present an analytical model for a single-link book-ahead bandwidth scheduler, which responds to advance reservation requests with the first-available time interval in which a channel is available. The link is assumed to be divided into m channels, and time is discretized into intervals. Our proposed model is a non-homogeneous continuous-time Markov chain, which has an embedded discrete-time Markov chain. We solve the model for call congestion, mean scheduling delay, and link utilization. This model can be used by network designers to select the size of the reservation window, K, in time-interval units, corresponding to a desired set of values for the output metrics, for a given value of m. For example, when m is 8, increasing the reservation window beyond 4 intervals does not affect the call congestion or system utilization, but causes the mean scheduling delay to increase. We show with comparative simulations that our analytical model can be used as a solution for an M/D/m/p queueing system at moderate-to-high loads.