Analysis and Simulation of Queueing Models for Reservation Based Bandwidth Access with Large Propagation Delays

Motivated by reservation-based multiple access protocols in satellite networks, we consider discrete time queueing models in which the allocation of a server to the queue/s is based on delayed queue length information. Service allocations are made at frame boundaries, and in general a frame consists of several slots, each of which can carry one packet. We analyse a model in which the service allocation at each frame boundary is based on the most recently observed queue length. In this model the queue length process is a Markov chain of order $\Delta+1$, where $\Delta$ is the round trip delay in frame times. An interesting aspect of this model is that bandwidth allocations go to waste, since the queue to which bandwidth is allocated may not have that many packets. For the case of a single node, independent and identically distributed arrivals, and when each frame has one slot, we are able to obtain explicit expressions for the generating function of the stationary queue length. A decomposition formula similar that found in vacation models is shown to hold. We use simulations to study the case of multiple slots per frame, and the case of two nodes. We also examine a model in which the bandwidth scheduler bases its allocations on the most recently observed queue length, and on the past allocations already made. We show how the mean queue length, the coefficient of variation of queue length, and the average wasted reservations vary with arrival rate, and the round trip delay $\Delta$