Abstract. We consider two types of buffering policies that are used in network switches supporting Quality of Service (QoS). In the FIFO type, packets must be transmitted in the order in which they arrive; the constraint in this case is the limited buffer space. In the bounded-delay type, each packet has a maximum delay time by which it must be transmitted, or otherwise it is lost. We study the case of overloads resulting in packet loss. In our model, each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets.Our main contribution is a thorough investigation of some natural greedy algorithms in various models. For the FIFO model we prove tight bounds on the competitive ratio of the greedy algorithm that discards packets with the lowest value when an overflow occurs. We also prove that the greedy algorithm that drops the earliest packets among all low-value packets is the best greedy algorithm. This algorithm can be as much as 1.5 times better than the tail-drop greedy policy, which drops the latest lowest-value packets.In the bounded-delay model we show that the competitive ratio of any on-line algorithm for a uniform bounded-delay buffer is bounded away from 1, independent of the delay size. We analyze the greedy algorithm in the general case and in three special cases: delay bound 2, link bandwidth 1, and only two possible packet values.Finally, we consider the off-line scenario. We give efficient optimal algorithms and study the relation between the bounded-delay and FIFO models in this case.

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Abstract. We consider two types of buffering policies that are used in network switches supporting Quality of Service (QoS). In the FIFO type, packets must be transmitted in the order in which they arrive; the constraint in this case is the limited buffer space. In the bounded-delay type, each packet has a maximum delay time by which it must be transmitted, or otherwise it is lost. We study the case of overloads resulting in packet loss. In our model, each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets.Our main contribution is a thorough investigation of some natural greedy algorithms in various models. For the FIFO model we prove tight bounds on the competitive ratio of the greedy algorithm that discards packets with the lowest value when an overflow occurs. We also prove that the greedy algorithm that drops the earliest packets among all low-value packets is the best greedy algorithm. This algorithm can be as much as 1.5 times better than the tail-drop greedy policy, which drops the latest lowest-value packets.In the bounded-delay model we show that the competitive ratio of any on-line algorithm for a uniform bounded-delay buffer is bounded away from 1, independent of the delay size. We analyze the greedy algorithm in the general case and in three special cases: delay bound 2, link bandwidth 1, and only two possible packet values.Finally, we consider the off-line scenario. We give efficient optimal algorithms and study the relation between the bounded-delay and FIFO models in this case.

We study the number of steps required to reach a pure Nash equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related, and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, K distinct weights, and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (e.g., allowing the largest weight job to move first). A by-product of our results is establishing a connection between various scheduling models and the game-theoretic notion of potential games. We show that load balancing in unrelated machines is a generalized ordinal potential game, load balancing in related machines is a weighted potential game, and load balancing in related machines and unit weight jobs is an exact potential game.

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c aImproved Competitive Guarantees for QoS Buffering ABSTRACT We consider a network providing Differentiated Services (Diffserv), which allow Internet Service Providers (ISP's) to offer different levels of Quality of Service (QoS) to different traffic streams. We study two types of buffering policies that are used in network switches supporting QoS. In the FIFO type, packets must be transmitted in the order they arrive. In the uniform boundeddelay type, there is a maximum delay time associated with the switch and each packet must be transmitted within this time, or otherwise it is dropped. In both models, the buffer space is limited, and packets are lost when the buffer overflows. Each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets. Our main contribution is an algorithm for the FIFO model with arbitrary packet values that for the first time achieves a competitive ratio better than 2, namely 2 -epsilon for a constant epsilon > 0. We also describe an algorithm for the uniform bounded delay model which simulates our algorithm for the FIFO model, and show that it achieves the same competitive ratio. AbstractWe consider a network providing Differentiated Services (Diffserv), which allow Internet Service Providers (ISP's) to offer different levels of Quality of Service (QoS) to different traffic streams. We study two types of buffering policies that are used in network switches supporting QoS. In the FIFO type, packets must be transmitted in the order they arrive. In the uniform bounded-delay type, there is a maximum delay time associated with the switch and each packet must be transmitted within this time, or otherwise it is dropped. In both models, the buffer space is limited, and packets are lost when the buffer overflows. Each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets. Our main contribution is an algorithm for the FIFO model with arbitrary packet values that for the first time achieves a competitive ratio better than 2, namely 2 − for a constant > 0. We also describe an algorithm for the uniform bounded delay model which simulates our algorithm for the FIFO model, and show that it achieves the same competitive ratio.

Abstract. Wireless sensor networks have recently posed many new system building challenges. One of the main problems is energy conservation since most of the sensors are devices with limited battery life and it is infeasible to replenish energy via replacing batteries. An effective approach for energy conservation is scheduling sleep intervals for some sensors, while the remaining sensors stay active providing continuous service. In this paper we consider the problem of selecting a set of active sensors of minimum cardinality so that sensing coverage and network connectivity are maintained. We show that the greedy algorithm that provides complete coverage has an approximation factor of " ! , where is the number of sensor nodes. Then we present algorithms that provide approximate coverage while the number of nodes selected is a constant factor far from the optimal solution.

Abstract-Many high-speed routers today use Input-Queued (IQ) architectures with a crossbar switching fabric based on optical technology. Packets in the input queues are divided into cells of unit length and the goal is to find a schedule of minimum makespan that forwards all packets to the output ports. The problem is complicated since in optical switches so called configuration delay, that is the time required to reconfigure the switching fabric, is non-negligible with respect to the cell transmission time. We aim to design a scheduler whose complexity does not depend on the number of packets in the input queues. Thus, we focus on the Non-Preemptive Bipartite Scheduling (NPBS) problem, where each input queue is connected to each output port in at most one configuration. We demonstrate that the NPBS problem is NP-hard for any value of the configuration delay and approximation within a ratio smaller than 7/6 is NP-hard as well. For the offline version of the NPBS problem, we show that a simple greedy algorithm achieves an approximation factor of 2 for arbitrary configuration delay. Then we consider the online version of the NPBS problem, where the switch gathers the incoming traffic periodically and then schedules the accumulated batches (batch scheduling). We propose a scheduling algorithm which guarantees strict delay for any admissible traffic provided that the switch has a moderate speedup of two.