Dynamic Allocation Problems in Loss Network Systems with Advanced Reservation

Abstract: We consider a class of well-known dynamic resource allocation models in loss network systems with advanced reservation. The most important performance measure in any loss network system is to compute its blocking probability, i.e., the probability of an arriving customer in equilibrium finds a fully utilized system (thereby getting rejected by the system). In this paper, we derive upper bounds on the asymptotic blocking probabilities for such systems in high-volume regimes. There have been relatively few results on loss network systems with advanced reservation due to its inherent complexity. The theoretical results find applications in a wide class of revenue management problems in systems with reusable resources and advanced reservation, e.g., hotel room, car rental and workforce management. We propose a simple control policy called the improved class selection policy (ICSP) based on solving a continuous knapsack problem, similar in spirit to the one proposed in Levi and Radovanovic (2010). Using our results derived for loss network systems with advanced reservation, we show the ICSP performs asymptotically near-optimal in high-volume regimes.