Fair Queuing and Other Probabilistic Allocation Methods

A server processes one job per unit of time and randomly schedules the jobs requested by a given set of users; each user may request a different number of jobs. Fair queuing (Shenker 1989) schedules jobs in successive round-robin fashion, where each agent receives one unit in each round until his demand is met and the ordering is random in each round. Fair queuing *, the reverse scheduling of fair queuing, serves first (with uniform probability) one of the users with the largest remaining demand. We characterize fair queuing * by the combination of lower composition--LC--(the scheduling sequence is history independent), demand monotonicity--DM--(increasing my demand cannot result in increased delay) and two equity axioms, equal treatment ex ante--ETEA (two identical demands give the same probability distribution of service) and equal treatment ex post--ETEP (two identical demands must be served in alternating fashion). The set of dual axioms (in which ETEA and ETEP are unchanged) characterizes fair queuing. We also characterize the rich family of methods satisfying LC, DM, and the familiar consistency--CSY--axiom. They work by fixing a standard of comparison (preordering) between a demand of xi units by agent i and one of xj units by agent j. The first job scheduled is drawn from the agents whose demand has the highest standard.

Split-Proof Probabilistic Scheduling

If shortest jobs are served first, splitting a long job into smaller jobs reported under different aliases can reduce the actual wait until completion. If longest jobs are served first, the dual maneuver of merging several jobs under a single reported identity is profitable. Both manipulations can be avoided if the scheduling order is random, and users care only about the expected wait until completion of their job. The Proportional rule stands out among rules immune to splitting and merging. It draws the job served last with probabilities proportional to size, then repeats among the remaining jobs. Among split-proof scheduling rules constructed in this recursive way, it is characterized by either one of the three following properties: an agent with a longer job incurs a longer delay; total expected delay is at most twice optimal delay; the worst expected delay of any single job is at most twice the smallest feasible worst delay. A similar result holds within the natural family of separable rules.

Maximizing Service Reliability in Distributed Computing Systems with Random Node Failures: Theory and Implementation

In distributed computing systems (DCSs) where server nodes can fail permanently with nonzero probability, the system performance can be assessed by means of the service reliability, defined as the probability of serving all the tasks queued in the DCS before all the nodes fail. This paper presents a rigorous probabilistic framework to analytically characterize the service reliability of a DCS in the presence of communication uncertainties and stochastic topological changes due to node deletions. The framework considers a system composed of heterogeneous nodes with stochastic service and failure times and a communication network imposing random tangible delays. The framework also permits arbitrarily specified, distributed load-balancing actions to be taken by the individual nodes in order to improve the service reliability. The presented analysis is based upon a novel use of the concept of stochastic regeneration, which is exploited to derive a system of difference-differential equations characterizing the service reliability. The theory is further utilized to optimize certain load-balancing policies for maximal service reliability; the optimization is carried out by means of an algorithm that scales linearly with the number of nodes in the system. The analytical model is validated using both Monte Carlo simulations and experimental data collected from a DCS testbed

Low-Latency Millimeter-Wave Communications: Traffic Dispersion or Network Densification?

This paper investigates two strategies to reduce the communication delay in future wireless networks: traffic dispersion and network densification. A hybrid scheme that combines these two strategies is also considered. The probabilistic delay and effective capacity are used to evaluate performance. For probabilistic delay, the violation probability of delay, i.e., the probability that the delay exceeds a given tolerance level, is characterized in terms of upper bounds, which are derived by applying stochastic network calculus theory. In addition, to characterize the maximum affordable arrival traffic for mmWave systems, the effective capacity, i.e., the service capability with a given quality-of-service (QoS) requirement, is studied. The derived bounds on the probabilistic delay and effective capacity are validated through simulations. These numerical results show that, for a given average system gain, traffic dispersion, network densification, and the hybrid scheme exhibit different potentials to reduce the end-to-end communication delay. For instance, traffic dispersion outperforms network densification, given high average system gain and arrival rate, while it could be the worst option, otherwise. Furthermore, it is revealed that, increasing the number of independent paths and/or relay density is always beneficial, while the performance gain is related to the arrival rate and average system gain, jointly. Therefore, a proper transmission scheme should be selected to optimize the delay performance, according to the given conditions on arrival traffic and system service capability