We introduce the problem of managing a FIFO buffer of bounded space, where arriving packets have dependencies among them. Our model is motivated by the scenario where large data frames must be split into multiple packets, because maximum packet size is limited by data-link restrictions. A frame is considered useful only if sufficiently many of its constituent packets are delivered. The buffer management algorithm decides, in case of overflow, which packets to discard and which to keep in the buffer. The goal of the buffer management algorithm is to maximize throughput of useful frames. This problem has a variety of applications, e.g., Internet video streaming, where video frames are segmented and encapsulated in IP packets sent over the Internet. We study the complexity of the above problem in both the offline and online settings. We give upper and lower bounds on the performance of algorithms using competitive analysis.

As more and more services are provided by servers via the Internet, Denial-of-Service (DoS) attacks pose an increasing threat to the Internet community. A DoS attack overloads the target server with a large volume of adverse requests, thereby rendering the server unavailable to ¿well-behaved¿ users. Recently, the novel paradigm of traffic ownership that enables the clients of Internet service providers (ISP) to configure their own traffic processing policies has gained popularity. In this paper, we propose two algorithms belonging to this paradigm that allow attack targets to dynamically filter their incoming traffic based on a distributed policy. The proposed algorithms defend the target against DoS and distributed DoS (DDoS) attacks and simultaneously ensure that it continues to receive valuable users' traffic. In a nutshell, a target can define a filtering policy which consists of a set of traffic classification rules and the corresponding amounts of traffic, measured in bandwidth units, which match each rule. The filtering algorithm is enforced by the ISP's or the Network Service Provider's (NSP) routers when a target is being overloaded with traffic. The goal is to maximize the amount of filtered traffic forwarded to the target, according to the filtering policy, from the ISP's or the NSP's network. The first algorithm we propose relies on complete collaboration among the ISP/NSP routers. It computes the filtering policy in polynomial time and delivers the best possible traffic mix to the target. The second algorithm is a distributed algorithm which assumes no collaboration among the ISP/NSP routers, each router only uses local information about its incoming traffic. We show the intuition behind the proof of lower bound on the second algorithm's worst-case performance.

The buffered crossbar switch architecture has recently gained considerable research attention. In such a switch, besides normal input and output queues, a small buffer is associated with each crosspoint. Due to the introduction of crossbar buffers, output and input contention is eliminated, and the scheduling process is greatly simplified. We analyze the performance of switch policies by means of competitive analysis, where a uniform guarantee is provided for all traffic patterns. We assume that each packet has an intrinsic value designating its priority and the goal of the switch policy is to maximize the weighted throughput of the switch. We consider FIFO queueing buffering policies, which are deployed by the majority of today's Internet routers. In packet-mode scheduling, a packet is divided into a number of unit length cells and the scheduling policy is constrained to schedule all the cells contiguously, which removes reassembly overhead and improves Quality-of-Service (QoS). For the case of variable length packets with uniform value density (Best Effort model), where the packet value is proportional to its size, we present a packet-mode greedy switch policy that is 7-competitive. For the case of unit size packets with variable values (Differentiated Services model), we propose a preemptive greedy switch policy that achieves a competitive ratio of 21. As far as we know, this is the first constant-competitive FIFO policy for this architecture in the case of variable value packets. The presented policies are simple and thus can be efficiently implemented at high speeds. Moreover, our results hold for any value of the internal switch fabric speedup.

We consider buffer management policies for shared memory switches. We study the case of overloads resulting in packet loss, where the constraint is the limited shared memory capacity. The goal of the buffer management policy is that of maximizing the number of packets transmitted. The problem is online in nature, and thus we use competitive analysis to measure the performance of the buffer management policies. Our main result is to show that the well-known preemptive Longest Queue Drop ( LQD ) policy is at most 2-competitive and at least √2-competitive. We also demonstrate a general lower bound of 4/3 on the performance of any deterministic online policy. Finally, we consider some other popular non-preemptive policies including Complete Partition, Complete Sharing, Static Threshold and Dynamic Threshold and derive almost tight bounds on their performance.

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.

Many high-speed routers today use input-queuing (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 nonpreemptive 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. We propose a scheduling algorithm that guarantees strict delay for any admissible traffic, provided that the switch has a moderate speed-up of two. Finally, we extend our results to the nonbipartite scheduling problem.

We consider a game that models the creation of a wireless ad hoc network, where nodes are owned by selfish agents. We study a novel cost sharing model in which agents may pay for the transmission power of the other nodes. Each agent has to satisfy some connectivity requirement in the final network and the goal is to minimize its payment with no regard to the overall system performance. We analyze two fundamental connectivity games, namely broadcast and convergecast. We study pure Nash equilibria and quantify the degradation in the network performance called the price of anarchy resulting from selfish behavior. We derive asymptotically tight bounds on the price of anarchy for these games. We also study centralized network design. One of the most important problems in wireless ad hoc networks is the minimum-energy broadcast. Recently, there appeared many new applications such as real-time multimedia, battlefield communications and rescue operations that impose stringent end-to-end latency requirement on the broadcasting time. However, the existing algorithms that minimize the broadcasting energy tend to produce solutions with high latency. We consider the problem of bounded-hop broadcast. We present approximation algorithms for this problem.

Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via backbone nodes. One common way of constructing such a backbone is based on the construction of a connected dominating set (CDS). In this article we present a very simple distributed algorithm for computing a small CDS. Our algorithm has an approximation factor of at most 6.91, improving upon the previous best-known approximation factor of 8 due to Wan et al. [2002]. The improvement relies on a refined analysis of the relationship between the size of a maximal independent set and a minimum CDS in a unit disk graph. This subresult also implies improved approximation factors for many existing algorithm.

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.

This paper considers the problem of packet-mode scheduling of input queued switches. Packets have variable lengths, and are divided into cells of unit length. Each packet arrives to the switch with a given deadline by which it must traverse the switch. A packet successfully passes the switch if the sequence of cells comprising it is contiguously transmitted out of the switch before the packet's deadline expires. A packet transmission may be preempted and restarted from the beginning later. The scheduling policy has to decide at each time step which packets to serve. The problem is online in nature, and thus we use competitive analysis to measure the performance of our scheduling policies.First we consider the case where the goal of the switch policy is to maximize the total number of successfully transmitted packets. We derive two algorithms achieving the competitive ratios of (22√log L +1) and N+ 1, respectively, where L is the ratio between the longest and the shortest packet lengths and N is the number of input/output ports. We also show that any deterministic online algorithm has a competitive ratio of at least (⌊log L⌋ + 1, N).Then we study the general case in which each packet has an intrinsic value representing its priority, and the goal is to maximize the total value of successfully transmitted packets. We derive an algorithm which achieves a competitive ratio of 2κ+2√κ+1/2+ (2κ+√κ+1/2+1) (√κ+1/2+3), where κ is the ratio between the maximum and the minimum value per cell. We note that [4] gives a lower bound of Ω(κ) on the performance of any deterministic online algorithm. In particular, our algorithm achieves a competitive ratio of approximately 11.123 for κ=1, which improves upon the previous best-known upper bound for this problem [17].We complement our results by studying the offline version of the problem, which is NP-hard We give a pseudo-polynomial 3-approximation algorithm for the general case and a polynomial 3-approximation algorithm for the case of unit value packets.

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.

The main objectives of a congestion control algorithm are high bandwidth utilization, fairness and responsiveness in changing environment. However, these objectives are contradicting in particular situations since the algorithm has to constantly probe available bandwidth, which may affect its stability. This paper proposes a novel congestion control algorithm that achieves high bandwidth utilization providing fairness among competing connections and, on the other hand, is sufficiently responsive to changes of available bandwidth. The main idea of the algorithm is to use adaptive setting for the additive increase/multiplicative decrease (AIMD) congestion control scheme, where parameters may change dynamically, with respect to the current network conditions.

Consider an Internet service provider (ISP), or a corporate intranet, that connects a large number of users with the Internet backbone using an "uplink." Within such a system, consider the traffic oriented towards the uplink, namely the streams whose start points are the local users and whose destination is outside the local domain. These streams are merged by a network that consists of merge nodes, typically arranged in a tree topology whose root is directly connected to the uplink. Without loss of generality, we may assume that the bandwidth of the link emanating from a merge node is less than the sum of bandwidths of incoming links (otherwise, we can assume that the incoming links are connected directly to the next node up). Hence, when all users inject data at maximum local speed, packets will eventually be discarded. A very effective way to mitigate some of the losses due to temporary overloads is to equip the merge nodes with buffers, that can absorb transient bursts by storing incoming packets while the outgoing link is busy. The merge nodes are controlled by local on-line buffer management algorithms whose job is to decide which packets to forward and which to drop so as to minimize the damage in case of an overflow.

Combined input and output queued (CIOQ) architectures with a moderate fabric speedup S>1 have come to play a major role in the design of high performance switches. The switch policy that controls such switches must consist of two components. A buffer management policy that controls admission to buffers, and a scheduling policy that schedules the transfer of packets from input buffers to output buffers. The goal of the switch policy is to maximize the throughput of the switch. When all packets have a uniform value (or importance), this corresponds to the number of packets sent from the switch. When packets have variable values, this corresponds to the total value of the packets sent.We mainly consider switches with virtual output queuing (VOQ) at the inputs. For the case of packets with uniform values we present a switch policy that is 3-competitive for any speedup. For the case of packets with variable values we propose two preemptive switch policies. One achieves a competitive ratio of 4S, and the other achieves a competitive ratio of 8min(k, 2log α), where k is the number of distinct packet values and α is the ratio between the largest and smallest values.

We introduce a new general scheme for shared memory nonpreemptive scheduling policies. Our scheme utilizes a system of inequalities and thresholds and accepts a packet if it does not violate any of the inequalities. We demonstrate that many of the existing policies can be described using our scheme, thus validating its generality. We propose a new scheduling policy, based on our general scheme, which we call the harmonic policy. Our simulations show that the harmonic policy both achieves high throughput and easily adapts to changing load conditions. We also perform a theoretical analysis of the harmonic policy and demonstrate that its throughput competitive ratio is almost optimal.

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.

We consider two types of buffering policies that are used in network switches supporting QoS (Quality of Service). In the FIFO type, packets must be released in the order they arrive; the difficulty 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 released, or otherwise it is lost. We study the cases where the incoming streams overload the buffers, resulting in packet loss. In our model, each packet has an intrinsic value; the goal is to maximize the total value of packets transmitted

Scheduling ATM cells schemes for an (optical) ATM switch can dramatically influence the performance of the ATM communication network. We present an efficient scheduling that is based on perfect bipartite matching. The algorithm ensures fairness, providing a guaranteed latency bound for each arriving cell.

Motivated by the special characteristics of multimedia tasks, we consider non-preemptive scheduling of tasks where there exists no (or very limited) information concerning the tasks before they are released. We present impossibility results and analyze algorithms for non-preemptive scheduling in single processor and multiprocessor systems. In particular, one set of our results considers the competitive ratio of the scheduling algorithm when the length of the tasks is not greater than C/sub max/ (and not smaller than C/sub min/). We show that the performance of a scheduling algorithm is improved dramatically when the release time of the tasks is O(C/sub max/) prior to their deadline; achieving a competitive ratio that is close to one.