The loss probability in queueing systems is a very useful metric in the design and analysis of high-speed communication networks. In this paper, we investigate the convexity properties of this metric for the finite-buffer, single server M=M=1=K queue. We demonstrate that the loss probability in the M=M=1=K queue is convex with respect to the traffic intensity (arrival rate) for values of the traffic intensity below a certain value ae (K) and is concave for values of the traffic intensity larger than ae (K). We establish several useful properties of ae (K). Second, we show that the loss probability is convex with respect to the service rate. Last, we show that the throughput is jointly concave in the arrival and service rates while the loss rate is jointly convex with respect to the same. KEYWORDS: M=M=1=K QUEUE; CONVEXITY OF PERFORMANCE MEASURES; LOSS SYSTEM. 1 This work is supported in part by the National Science Foundation under grant NCR-9116183 2 Dept. of Elect. and C...

In this paper we consider the problem of minimizing the costs of outsourcing warranty repairs when failed items are dynamically routed to one of several service vendors. In our model, the manufacturer incurs a repair cost each time an item needs repair and also incurs a goodwill cost while an item is awaiting and undergoing repair. For a large manufacturer with annual warranty costs in the tens of millions of dollars, even a small relative cost reduction from the use of dynamic (rather than static) allocation may be practically significant. However, due to the size of the state space, the resulting dynamic programming problem is not exactly solvable in practice. Furthermore, standard routing heuristics, such as join-theshortest-queue, are simply not good enough to identify potential cost savings of any significance. We use two different approaches to develop effective, simply structured index policies for the dynamic allocation problem. The first uses dynamic programming policy improvement while the second deploys Whittle’s proposal for restless bandits. The closed form indices concerned are new and the policies sufficiently close to optimal to provide cost savings over static allocation. All results of this paper are demonstrated using a simulation study.

The nonstationary Erlang loss model is a queueing system consisting of a finite number of servers and no waiting room with a nonstationary arrival process or a time-dependent service rate. The Erlang loss model is commonly used to model and evaluate many communication systems. Often, these types of service systems encounter a change in the arrival rate over time while the service rate remains either constant or changes very little over time. In view of this, the focus in this research is the nonstationary Erlang loss queues and network with time-dependent arrival rate and constant service rate. We developed an iterative scheme referred to as the fixed point approximation (FPA) in order to obtain the time-dependent blocking probability and other measures for a single-class nonstationary Erlang loss queue and a nonstationary multi-rate Erlang loss queue. The FPA method was compared against exact numerical results, and two other methods, namely, MOL and PSA, for various nonstationary Erlang loss queues with sinusoidal arrival rates. Although we used sinusoidal functions to model the time-dependent arrival rate, the solution can be obtained for any arrival rate function. Experimental results demonstrate that the FPA

Abstract — We show that when memory is bounded, i.e. buckets are finite, dynamic hash tables that allow insertions and deletions behave significantly worse than their static counterparts that only allow insertions. This behavior differs from previous results in which, when memory is unbounded, the two models behave similarly. We show the decrease in performance in dynamic hash tables using several hash-table schemes. We also provide tight upper and lower bounds on the achievable overflow fractions in these schemes. Finally, we propose an architecture with contentaddressable memory (CAM), which mitigates this decrease in performance. A. Background I.

The nonstationary loss queue is of great interest since the arrival rate in most communication systems varies over time. In view of the difficulty in solving the nonstationary loss queue, various approximation methods have been developed. In this paper, we review several of these approximation methods and present a new technique, the fixed point approximation (FPA) method. Numerical evidence points to the fact that the FPA method gives the exact solution. 1.

The loss probability in queueing systems is a very useful metric in the design and analysis of high-speed communication networks. In this paper, we investigate the convexity properties of this metric for the finite-buffer, single server M=M=1=K queue. We demonstrate that the loss probability in the M=M=1=K queue is convex with respect to the traffic intensity (arrival rate) for values of the traffic intensity below a certain value ae (K) and is concave for values of the traffic intensity larger than ae (K). We establish several useful properties of ae (K). Second, we show that the loss probability is convex with respect to the service rate. Last, we show that the throughput is jointly concave in the arrival and service rates while the loss rate is jointly convex with respect to the same. KEYWORDS: M=M=1=K QUEUE; CONVEXITY OF PERFORMANCE MEASURES; LOSS SYSTEM. 1 This work is supported in part by the National Science Foundation under grant NCR-9116183 2 Dept. of Elect. and Comp....

Optimal flow control problems of multiple-server (M/M/m) queueing systems are studied. Due to enhanced flexibility of the decision making, intuitively, we expect that grouping together separated systems into one system provides improved performance over the previously separated systems. This paper presents a counter-intuitive result. We consider a noncooperative optimal flow control problem of M/M/m queueing systems where each player strives to optimize unilaterally its own power where the power of a player is the quotient of the throughput divided by the mean response time for the player. We report a counter-intuitive case where the power of every user degrades after grouping together K(> 1) separated M/M/N systems into a single M/M/(KN)system.

Abstract—Hash-based data structures, which use randomization in order to represent efficiently a list of elements, are one of the most-used data structures in networking applications, where both time and fast memory are scarce resources. This paper investigates the realistic scenario in which elements are not only added to the data structure but also deleted. We show that when the memory is bounded, dynamic hash-tables with deletions behave significantly worse than their static counterparts. This is contrast with previous results that show that when the memory is not bounded the two models behave practically the same. We provide tight upper and lower bounds on the achievable overflow fraction of the scheme under various models and system parameters. Then, we propose two architectures using CAMs and TCAMs that allow us to mitigate this decrease in performance. Our analytical results are confirmed using simulations with reallife traces and real hash-functions. A. Background I.