Multi-chip multicast schedulers in input-queued switches

The delay and throughput characteristics of a packet switch depend mainly on the queueing scheme and the scheduling algorithm deployed at the switch. Early research on scheduling algorithms has mainly focused on maximum weight matching scheduling algorithms. It is known that maximum weight matching algorithms guarantee the stability of input-queued switches, but are impractical due to their high computational complexity. Later research showed that the less complex maximal matching algorithms can stabilize input-queued switches when they are deployed with a speed-up of two. For practical purposes, neither a high computational complexity nor a speed-up of two is desirable.In this paper, we investigate the application of matching algorithms that approximate maximum weight matching algorithms to scheduling problems. We show that while having a low computational complexity, they guarantee the stability of input queued switches when they are deployed with a moderate speed-up.In particular, we show that the improve_matching algorithm stabilizes input-queued switches when it is deployed with a speed-up of 3<over>2+ε.In a second step, we further improve on these results by proposing a class of maximal weight matching algorithms that stabilize an input-queued switch without any speed-up.Whereas initial research has only focused on scheduling algorithms that guarantee the stability of a single switch, recent work has shown how scheduling algorithms for single switches can be modified in order to design distributed scheduling algorithms that stabilize networks of input-queued switches. Using those results, we show that the switching algorithms proposed in this paper do not only stabilize a single switch, but also networks of input-queued switches.

Summary form only given. Multicast communication, which involves transmitting information from one node to multiple nodes, is a vital operation in both broadband integrated services digital networks (BISDN) and scalable parallel computers. Among different multicast switching networks, much work has been centered around the crossbar switches due to the simplicity of implementation. However, crossbars have the maximum number of crosspoints and implementation complexity among all switching fabrics. Multistage interconnect networks (MINs) such as Clos networks have attracted many attentions in recent years due to the nonblocking property as the crossbars, while at the same time possessing many advantages over crossbars. However, no multicast scheduling and routing algorithm have been applied to Clos network. This paper explores this aspect - we study some existing multicast scheduling and routing algorithms and apply them to Clos networks. Moreover, we propose two packet scheduling strategies to improve the system performance in terms of switch blocking probability and throughput, as shown by simulations.

High-speed routers and high-performance data centers share a common system-level architecture in which multiple processing nodes are connected by an interconnection network for high-speed communications. Load balancing is an important technique for maximizing throughput and minimizing delay of the interconnection network. In this thesis, efficient load balancing schemes are designed and analyzed for next-generation routers and data centers.
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\nIn high-speed router design, two preferred switch architectures are input-queued switch and load-balanced switch. In an input-queued switch, time-domain load balancing can be carried out by an iterative algorithm that schedules packets for sending in different time slots. The complexity of an iterative algorithm increases rapidly with the number of scheduling iterations. To address this problem, a single-iteration scheduling algorithm called D-LQF is designed, in which exhaustive service policy is adopted for reusing the matched input-output pairs in the previous time slots to grow the match size. 
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\nUnlike an input-queued switch, a load-balanced switch consists of two stages of crossbar switch fabrics, where load balancing is carried out in both time and space domains. Among various load-balanced switches, the feedback-based switch gives the best delay-throughput performance. In this thesis, the feedback-based switch is enhanced in three aspects. Firstly, we focus on reducing its switch fabric complexity. Instead of using crossbars, a dual-banyan network is proposed. The complexity of dual-banyan can be further reduced by merging the two banyans to form a Clos network, resulting in a Clos-banyan network. Secondly, we target at improving the delay performance of the feedback-based switch. A Clos-feedback switch architecture is devised where each switch module in the Clos network is a small feedback-based switch. With application-flow based load balancing, packet order is ensured and the average packet delay is reduced from O(N) to O(n), where N and n are the switch and switch module sizes, respectively. Thirdly, we extend the feedback-based switch to support multicast traffic. Based on the notion of pointer-based multicast VOQ, an efficient multicast scheduling algorithm with packet replication at the middle-stage ports only is proposed. In order to provide close-to-100% throughput for any admissible multicast traffic patterns, a three-stage implementation of feedback-based switch is also designed.
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\nIn designing load balancing schemes for data centers, we focus on the most popular fat-tree based data centers. Notably, packet-based load balancing is widely considered infeasible for data centers. This is because the associated packet out-of-order problem will cause unnecessary TCP fast retransmits, and as a result, severely undermine TCP performance. In this thesis, we show that if packet-based load balancing is performed properly, the packet out-of-order problem can be easily addressed by slightly increasing the number of duplicate ACKs required for triggering fast retransmit. Admittedly, in case of a real packet loss, the loss recovery time will be increased. But our simulation results show that such an increase is far less than the reduction in the network queueing delay (due to a better load-balanced network). As compared to a flow-based load balancing scheme, our packet-based scheme consistently provides significantly higher goodput and noticeably smaller delay.

In this paper, we consider scheduling in multicast switching networks, which aims to minimize the multicast latency for a set of multicast requests. Such a problem has been proved to be NP-complete. We propose a simple, fast greedy multicast scheduling algorithm and derive a lower bound and an upper bound on the performance of the algorithm. As can be seen, while a lower bound is fairly straightforward, the upper bound is much more difficult to obtain. By translating the multicast scheduling problem into a graph theory problem and employing a random graph approach, we are able to obtain a probabilistic upper bound on the performance of the multicast scheduling algorithm. Our analytical and simulation results show that the performance of the proposed multicast scheduling algorithm is quite close to the lower bound and is statistically guaranteed by the probabilistic upper bound.

Assigning jobs to optimum resources in a grid environment is the main aim of a grid scheduler. Communication cost has always been an important issue in grid environments. Proposing new scheduling algorithms to consider this cost accurately and allocate jobs to an optimum resource efficiently has always been of great importance. In this paper we have proposed a grid scheduling algorithm that is aware of the costs for different network paths. We have also considered soft real-time characteristics of jobs in our proposed algorithm. We have simulated and compared our algorithm with some key scheduling algorithms such as Least Load First (LLF), Random, and First Come First Served (FCFS) in Gridsim by considering soft real-time jobs. Results show the superiority of our scheduling algorithm due to its ability to predict network cost and to satisfy the demands of soft real-time tasks.

Layered multicast is a scalable solution to data dissemination in heterogeneous networks such as the Internet. In this paper, we study the scheduling problem arising in the layered multicast context. Our goal is to generate a multicast schedule for two different objectives, i.e., to minimize the weighted sum (the L 1 objective) of the per-layer average waiting time, and to minimize the maximum approximation ratio (the L ∞ objective) of the subschedules on individual layers. Compared to the previous work on multicast scheduling, this paper addresses the data popularity and the interaction among layers simultaneously. We present a simple randomized algorithm for both objectives of the layered multicast scheduling problem. For the L 1 objective, we provide a deterministic 2-approximation algorithm for the general multi-layer cases. For the L ∞ objective, we present an algorithm for the two-layer case which is 1.6875-approximation ignoring an additive constant.

Recent developments in networking technologies, coupled with the advent of high-capacity storage devices and improved coding schemes, will make it feasible to provide many advanced multimedia communications services. Among future telecommunication services, the VOD (Video On Demand) service is emerging as one of the most promising services. In this paper, we propose a new VOD service scheme that utilizes the dynamic multicasting capabilities of future networks. We first describe an overall VOD service architecture that consists of CPEs (Customer Premise Equipments), SCCs (Service Control Centers), and ISs (Information Stores). Based on the assumptions that each subscriber has local storage space and the video transfer speed is faster than the playback speed, we develop a new service scheme where video signals are multicasted to multiple subscribers simultaneously. To realize the potential benefits of multicasting, we propose two scheduling algorithms: EDS (Earliest Deadline Scheduling) and MMS (Most Multicasting Scheduling). Finally, we study the performance of multicasting scheme and compare the performance of the two scheduling algorithms via computer simulation. The simulation results show that multicasting increases the service capacity of an SCC significantly.

Due to its simplicity and scalability, the differentiated services (DiffServ) model is expected to be widely deployed across the Internet. For each DiffServ compliant router, the scheduling algorithm is critical in implementing per hop behaviors (PHBs), according to which packets are forwarded. We propose a hierarchical DiffServ scheduling (HDS) algorithm to support DiffServ classes on input-queued switches. The proposed HDS algorithm features in a hierarchical scheduling scheme that consists of two levels of schedulers. One level is the central scheduler which is designed to maximize the switch throughput by computing a maximal size matching between input ports and output ports. The other level is formed by input port schedulers which provide differentiated services by serving cells belonging to different classes dynamically. Using such a hierarchical scheme, the implementation complexity and the amount of information needed to be transmitted between input ports and the central scheduler are dramatically reduced compared with existing maximal weight matching based DiffServ scheduling algorithms. The tradeoff of its slightly worse delay performance is acceptable.

Interplanetary round trip mission design

Input-Queued switching fabrics are widely used in high speed network switches for their scalability. However, a scheduling algorithm must be elaborative designed for input-queued switches to get high throughput. The randomized algorithms are attractive in kinds of scheduling algorithms for their low complexity and well performance. In this paper, a fluid model is introduced to analyze the rate stability of switching systems with randomized schedulers. By this method, we proved that the randomized scheduling algorithm can achieve 100% throughput under any admissible traffics which satisfy the strong law of large numbers (SLLN).

The input-queued switch with service class priority is becoming an attractive solution for high-bandwidth ATM switches. In previous related work (see Motoyama, S. et al., IEEE Comm. Letters, vol.3, no.12, p.323-5, 1999), it has been proved that throughput achieves almost 100% for up to 92% of the offered load when random access buffers and a round robin scheduling algorithm are used. However, this is only a theoretical result: the round robin scheduling algorithm is too complex to implement in hardware. We introduce a modification through a scheduling algorithm called iterative longest port first with throughput maximization (iLPFwTM) which is proposed to overcome the complexity of the previous solution regarding its hardware implementation at high speed. A performance analysis is carried out by simulation and the results show a better performance in comparison with the recent ATM input-queued switch with round robin schedulers and service class priority. It means that the ATM input-queued switch with iLPFwTM scheduler and service class priority is proved to be more attractive for high-bandwidth ATM switch implementation than the solution based on a round robin scheduling algorithm.

Several dynamic bandwidth allocation algorithms have been introduced to schedule upstream wavelength channels in wavelength division multiplexing Ethernet passive optical networks (WDM EPONs), but mostly for homogenous WDM EPON networks with the same distance between each optical network unit (ONU) and the optical line terminal. For WDM EPON with heterogeneous round trip times (RTTs), we propose two algorithms for ONU scheduling, called nearest first and early allocation (EA); and a wavelength assignment algorithm, called best fit (BF). Both ONU scheduling algorithms take RTT dissimilarities into account, thus minimizing packet delay and packet drop ratio at ONUs. Additionally, EA can relive the common drawback of offline scheduling, i.e., channel idle time. On the other hand, the BF wavelength assignment is proposed that assigns the best wavelength to each ONU in order to improve network performances in terms of packet queuing delay and packet drop ratio at ONU sides.

The round trip time is the basis for designing elevator systems. There are a number of different methods for calculating the round trip time, whether analytical or numerical. As the building and the conditions of the traffic become more complicated, analytical methods become intractable. Numerical methods offer an attractive alternative for calculating the round trip time. Monte Carlo simulation has been used to find the value of the round trip time. The use of the Markov chain Monte Carlo method is a viable alternative. This paper derives the formulae necessary to build the transition probability matrix for the elevator during a round trip under incoming traffic conditions and multiple entrances. A numerical example is then solved by finding the round trip time using the Markov chain Monte Carlo method and then cross verified by the use of Monte Carlo simulation and the analytical equation based method. Excellent agreement has been found between the three methods, with differences smaller than 0.01%.

The evaluation of the round trip time ( τ) still forms the basis for the design of elevator traffic systems. The elevator round trip time is the time taken for the elevator to complete a full cycle of the building, picking up passengers from their origin floors and dropping them off at their destination floors. It is assumed that the elevator car transports P passengers from their origins to their destinations during one round trip. By dividing the value of the round trip time by the target interval, the required number of elevators in the group can be found and fed into the overall traffic design. Traditionally, simplified formulae have been used to evaluate the value of the round trip time under a number of simplifying assumptions. This paper develops the formulae for the most general case of mixed traffic conditions, whereby every floor can be an occupant floor and an exit/entrance floor (i.e. every floor can have a percentage population, U( i), and a percentage arrival rate, Parr( i)). However, the formulae developed make a simplification by assuming a constant passenger arrival model, rather than the widely accepted Poisson passenger arrival model. The new developed set of formulae comprises three parts: the kinematic part ( τK), the door part ( τS) and the passenger transfer part ( τP). The kinematic part in turn comprises six components: the up journey ( UJ) time; the down journey ( DJ) time; the upper connecting journey ( UCJ) time; the lower connecting journey ( LCJ) time; the down return journey ( DRJ) time; and the up return journey ( URJ) time. The derivation process is accompanied by stepwise verification of all the different components of the round trip time using the Monte Carlo simulation (MCS) method. The results of the formulae match those from the MCS to less than 0.0025%. Practical application: Engineers usually design elevator traffic systems under up-peak traffic conditions, where only incoming traffic is assumed. It is sometimes useful to assess the design under a mixture of traffic conditions (e.g. lunchtime conditions). The formulae developed in this paper can thus be used to allow the designer to evaluate the round trip time under a mixture of traffic conditions. In practice, the formulae would not be evaluated by hand, but implemented as a software programme. Once the designer has evaluated the round trip time under the specified mix of traffic conditions (e.g. 40% incoming traffic; 40% outgoing traffic; 20% inter-floor traffic), then he/she can divide that number by the target interval to find the required number of elevators. This result can then be compared to the required number of elevators under up-peak conditions to assess the adequacy of the design for these mixed traffic conditions.

An integrated scheduling and buffer management scheme for input queued switches with finite buffer space