Alexander Kesselman

Convergence time to Nash equilibria

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 (such as allowing the largest weight job to move first).

Buffer Overflow Management in QoS Switches

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.

Improved approximation algorithms for connected sensor cover

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 no better than Ω(log n), where n 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. Finally, we show how to connect a set of sensors that already provides coverage.

Fast distributed algorithm for convergecast in ad hoc geometric radio networks

Wireless ad hoc radio networks have gained a lot of attention in recent years. We consider geometric networks, where nodes are located in a euclidean plane. We assume that each node has a variable transmission range and can learn the distance to the closest neighbor. We also assume that nodes have a special collision detection (CD) capability so that a transmitting node can detect a collision within its transmission range. We study the basic communication problem of collecting data from all nodes called convergecast. We measure the latency of convergecast, that is the number of time steps needed to collect the data in any n-node network. We propose a very simple randomized distributed algorithm that has the expected running time O(log n). We also show that this bound is tight and any algorithm needs Ω(log n) time steps while performing convergecast in an arbitrary network. One of the most important problems in wireless ad hoc networks is to minimize the energy consumption, which maximizes the network lifetime. We study the trade-off between the energy and the latency of convergecast. We show that our algorithm consumes at most O(n log n) times the minimum energy. We also demonstrate that for a line topology the minimum energy convergecast takes n - 1 time steps while any algorithm performing convergecast within O(log n) time steps requires Ω(n) times the minimum energy.

Competitve buffer management for shared-memory switches

We consider buffer management policies for shared memory packet switches supporting Quality of Service (QoS). There are two interesting dimensions in which the setting may different. The first is the packet size, whether all the packets of the same fixed size or do packets have variable length. The second is the value of the packets, do all the packets have the same value or do different packets have different values. The goal of the buffer management policy is to maximize the total value of packets transmitted. Our main result is to show that the well-known Longest Queue Drop (LQD) policy in 2-competitive and at least √2-competitive for the case of fixed size and value packets. We also show a 4/3 general lower bound on the competitiveness in this case. We extend the results to the case of variable size fixed value packets, and derive a slightly worse bound. For the case of variable value we derive randomized policy whose competitive ratio in logarithmic on the ratio of the maximal to minimal value.

Game-Theoretic analysis of internet switching with selfish users

We consider the problem of Internet switching, where traffic is generated by selfish users. We study a packetized (TCP-like) traffic model, which is more realistic than the widely used fluid model. We assume that routers have First-In-First-Out (FIFO) buffers of bounded capacity managed by the drop-tail policy. The utility of each user depends on its transmission rate and the congestion level. Since selfish users try to maximize their own utility disregarding the system objectives, we study Nash equilibria that correspond to a steady state of the system. We quantify the degradation in the network performance called the price of anarchy resulting from such selfish behavior. We show that for a single bottleneck buffer, the price of anarchy is proportional to the number of users. Then we propose a simple modification of the Random Early Detection (RED) drop policy, which reduces the price of anarchy to a constant.

Fast Distributed Algorithm for Convergecast in Ad Hoc Geometric Radio Networks

Wireless ad hoc radio networks have gained a lot of attention in recent years. We consider geometric networks, where nodes are located in a euclidean plane. We assume that each node has a variable transmission range and can learn the distance to the closest neighbor. We also assume that nodes have a special collision detection (CD) capability so that a transmitting node can detect a collision within its transmission range. We study the basic communication problem of collecting data from all nodes called convergecast. We measure the latency of convergecast, that is the number of time steps needed to collect the data in any n-node network. We propose a very simple randomized distributed algorithm that has the expected running time O(log n). We also show that this bound is tight and any algorithm needs Ω(log n) time steps while performing convergecast in an arbitrary network. One of the most important problems in wireless ad hoc networks is to minimize the energy consumption, which maximizes the network lifetime. We study the trade-off between the energy and the latency of convergecast. We show that our algorithm consumes at most O(n log n) times the minimum energy. We also demonstrate that for a line topology the minimum energy convergecast takes n - 1 time steps while any algorithm performing convergecast within O(log n) time steps requires Ω(n) times the minimum energy.

Optimizing TCP retransmission timeout

Delay spikes on Internet paths can cause spurious TCP timeouts leading to significant throughput degradation. However, if TCP is too slow to detect that a retransmission is necessary, it can stay idle for a long time instead of transmitting. The goal is to find a Retransmission Timeout (RTO) value that balances the throughput degradation between both of these cases. In the current TCP implementations, RTO is a function of the Round Trip Time (RTT) alone. We show that the optimal RTO that maximizes the TCP throughput need to depend also on the TCP window size. Intuitively, the larger the TCP window size, the longer the optimal RTO. We derive the optimal RTO for several RTT distributions. An important advantage of our algorithm is that it can be easily implemented based on the existing TCP timeout mechanism.

Improved Competitive Performance Bounds for CIOQ Switches

Combined Input and Output Queued (CIOQ) architectures with a moderate fabric speedupS>1 have come to play a major role in the design of high performance switches. In this paper we study CIOQ switches with First-In-First-Out (FIFO) buffers providing Quality of Service (QoS) guarantees. The goal of the switch policy is to maximize the total value of packets sent out of the switch. We analyze the performance of a switch policy by means of competitive analysis, where a uniform worst-case performance guarantee is provided for all traffic patterns. Azar and Richter (ACM Trans. Algorithms 2(2):282–295, 2006) proposed the β-PG algorithm (Preemptive Greedy with a preemption factor of β) that is 8-competitive for an arbitrary speedup value when β=3. We improve upon their result by showing that this algorithm achieves a competitive ratio of 7.5 and 7.47 for β=3 and β=2.8, respectively. Basically, we demonstrate that β-PG is at most

Harmonic buffer management policy for shared memory switches

\frac{\beta^{2} + 2\beta}{\beta - 1}