Stochastic bandwidth packing process: Stability conditions via Lyapunov function technique

We consider the following stochastic bandwidth packing process: the requests for communication bandwidth of different sizes arrive at times t=0,1,2,... and are allocated to a communication link using "largest first" rule. Each request takes a unit time to complete. The unallocated requests form queues. Coffman and Stolyar [6] introduced this system and posed the following question: under which conditions do the expected queue lengths remain bounded over time (queueing system is stable)? We derive exact constructive conditions for the stability of this system using the Lyapunov function technique. The result holds under fairly general assumptions on the distribution of the arrival processes.