Asymptotic Blocking Probabilities in Loss Networks with Subexponential Demands

Abstract

The analysis of stochastic loss networks has long been of interest in computer and communications networks and is becoming important in the areas of service and information systems. In traditional settings, computing the well known Erlang formula for blocking probability in these systems becomes intractable for larger resource capacities. Using compound point processes to capture stochastic variability in the request process, we generalize existing models in this framework and derive simple asymptotic expressions for blocking probabilities. In addition, we extend our model to incorporate reserving resources in advance. Although asymptotic, our experiments show an excellent match between derived formulas and simulation results even for relatively small resource capacities and relatively large values of blocking probabilities.

Queuing with future information

“…In other application domains, the idea of exploiting future information or predictions to improve decision making has been explored. Advance reservations (a form of future information) have been studied in lossy networks [8,14] and, more recently, in revenue management [13]. Using simulations, [12] demonstrates that the use of a one-week and two-week advance scheduling window for elective surgeries can improve the efficiency at the associated intensive care unit (ICU).…”

“…By Lemma 11 and equations (6.28), we have max 1≤i≤K |E i | = o(K) a.s. (A. 14) framework of [20], which is based on a fluid model that heavily exploits the symmetry in the system. On the downside, however, the results in this paper tell us very little when system size N is small, in which case it is highly conceivable that a centralized scheduling rule, such as the longestqueue-first policy, can out-perform a collection of decentralized admissions control rules.…”