Round Robin Routing Research Articles

Optimal Round-Robin Routing to Parallel Servers in Heavy Traffic

We study a system with heterogeneous parallel servers. Upon arrival, a job is routed to the queue of one of the servers. We establish the diffusion limit for the round-robin (RR) policy, and show that with properly chosen parameters, it achieves the optimal performance asymptotically over all blind routing policies. Analysis of the diffusion limit yields a number of insights into the performance of the optimal RR policies.

Multiple Server SRPT With Speed Scaling Is Competitive

Can the popular shortest remaining processing time (SRPT) algorithm achieve a constant competitive ratio on multiple servers when server speeds are adjustable (speed scaling) with respect to the flow time plus energy consumption metric? This question has remained open for a while, where a negative result in the absence of speed scaling is well known. The main result of this paper is to show that multi-server SRPT with speed scaling can be constant competitive, with a competitive ratio that only depends on the power-usage function of the servers, but not on the number of jobs/servers or the job sizes (unlike when speed scaling is not allowed). When all job sizes are unity, we show that round-robin routing is optimal and can achieve the same competitive ratio as the best known algorithm for the single server problem. Finally, we show that a class of greedy dispatch policies, including policies that route to the least loaded or the shortest queue, do not admit a constant competitive ratio. When job arrivals are stochastic, with Poisson arrivals and i.i.d. job sizes, we show that random routing and a simple gated-static speed scaling algorithm achieves a constant competitive ratio.

CD-Xbar: A Converge-Diverge Crossbar Network for High-Performance GPUs

Modern GPUs feature an increasing number of streaming multiprocessors (SMs) to boost system throughput. How to construct an efficient and scalable network-on-chip (NoC) for future high-performance GPUs is particularly critical. Although a mesh network is a widely used NoC topology in manycore CPUs for scalability and simplicity reasons, it is ill-suited to GPUs because of the many-to-few-to-many traffic pattern observed in GPU-compute workloads. Although a crossbar NoC is a natural fit, it does not scale to large SM counts while operating at high frequency. In this paper, we propose the converge-diverge crossbar (CD-Xbar) network with round-robin routing and topology-aware concurrent thread array (CTA) scheduling. CD-Xbar consists of two types of crossbars, a local crossbar and a global crossbar. A local crossbar converges input ports from the SMs into so-called converged ports; the global crossbar diverges these converged ports to the last-level cache (LLC) slices and memory controllers. CD-Xbar provides routing path diversity through the converged ports. Round-robin routing and topology-aware CTA scheduling balance network traffic among the converged ports within a local crossbar and across crossbars, respectively. Compared to a mesh with the same bisection bandwidth, CD-Xbar reduces NoC active silicon area and power consumption by 52.5 and 48.5 percent, respectively, while at the same time improving performance by 13.9 percent on average. CD-Xbar performs within 2.9 percent of an idealized fully-connected crossbar. We further demonstrate CD-Xbar's scalability, flexibility and improved performance per Watt (by 17.1 percent) over state-of-the-art GPU NoCs which are highly customized and non-scalable.

Randomly prioritized buffer-less routing architecture for 3D Network on Chip

Recently, 3D NoC has become more important than 2D NoC due its new geometrical arrangement and also reduces the wire length from global interconnect to local interconnect. One of the main components to implement 3D NoC is the router. The components of the router are crossbar, FIFO, and arbiter. The scheduling algorithm is the main part of the arbiter which schedules and delivers all packets to the destination nodes without any loss of packets. Packets that have the highest priority are served first,the remaning highest priority packets ares queued in the priority register and non-priority packets are served after all priority packets are served. Round Robin routing algorithm is commonly used as the scheduling algorithm in most of the routers. This paper proposes a novel 3D lottery routing algorithm which is based on arbitral mechanism like randomly prioritized buffer. Communication among the IPs in NoC can be customized by users through the lottery router. The lottery routing algorithm distinguishes the different priorities of the input port and makes sure that it responses to the higher priority port. The efficient hardware implementation of 3D NoC is proposed using Xilinx Spartan 3E FPGA, the result shows that the proposed architecture consumes 1644 slices out of 4656 slices and operates at the maximum frequency of about 103.602MHz. The 3D NoC is modeled and implemented with a Cadence Electronic Design Automation tool and the results show that the power consumption of 3D NoC is reduced by 9% compared to a single layer.

On Round-Robin routing with FCFS and LCFS scheduling

We study the Round-Robin (RR) routing to a system of parallel queues, which serve jobs according to FCFS or preemptive LCFS scheduling disciplines. The cost structure comprises two components: a service fee and a queueing delay related component. With Poisson arrivals, the inter-arrival time to each queue obeys the Erlang distribution. This allows us to study the mean and transient behavior of the queues separately. The service fee is independent of the scheduling and queueing, and we obtain the corresponding mean cost rate and value function in closed forms. With respect to queueing delay, we first derive integral expressions enabling efficient computation of the corresponding size-aware value functions. By decomposition, these yield also the value function for the whole system of m parallel queues fed by RR. Given the value function, one can carry out the first policy iteration step with arbitrary holding cost rates (e.g., delay, slowdown, etc.) yielding efficient size-, cost- and state-aware policies. Moreover, the mean waiting and sojourn times in the corresponding systems get resolved at the same time. The results are demonstrated in the numerical examples, where we compute near optimal job routing policies for sample systems.

Static load-balanced routing for slimmed fat-trees

Slimmed fat-trees have recently been proposed and deployed to reduce costs in High Performance Computing (HPC) clusters. While existing static routing schemes such as destination-mod-k (D-mod-k) routing are load-balanced and effective for full bisection bandwidth fat-trees, they incur significant load imbalance in many slimmed fat-trees. In this work, we propose a static load balanced routing scheme, called Round-Robin Routing (RRR), for 2- and 3-level extended generalized fat-trees (XGFTs), which represent many fat-tree variations including slimmed fat-trees. RRR achieves near perfect load-balancing for any such XGFT in that links at the same level of a tree carry traffic from almost the same number of source–destination pairs. Our evaluation results indicate that on many slimmed fat-trees, RRR is significantly better than D-mod-k for dense traffic patterns due to its better load-balancing property, but performs worse for sparse patterns. We develop a combined routing scheme that enjoys the strengths of both RRR and D-mod-k by using RRR in conjunction with D-mod-k. The combined routing is a robust load-balanced routing scheme for slimmed fat-trees: it performs similar to D-mod-k for sparse traffic patterns and to RRR for dense patterns.

Tighter Worst-Case Bounds on Algebraic Gossip

Gossip and in particular network coded algebraic gossip have recently attracted attention as a fast, bandwidth-efficient, reliable and distributed way to broadcast or multicast multiple messages. While the algorithms are simple, involved queuing approaches are used to study their performance. The most recent result in this direction shows that uniform algebraic gossip disseminates k messages in O(Δ(D + k + log n)) rounds where D is the diameter, n the size of the network and Δ the maximum degree. In this paper we give a simpler, short and self-contained proof for this worst-case guarantee. Our approach also allows to reduce the quadratic Δ D term to min{3n, Δ D}. We furthermore show that a simple round robin routing scheme also achieves min{3n, Δ D} + Δ k rounds, eliminating both randomization and coding. Lastly, we combine a recent non-uniform gossip algorithm with a simple routing scheme to get a O(D + k + log^{O(1)}) gossip information dissemination algorithm. This is order optimal as long as D and k are not both polylogarithmically small.

Round robin scheduling of heterogeneous parallel servers in heavy traffic

We consider scheduling for heterogeneous server systems, where tasks arrive according to a Poisson process, with their processing requirements following a discrete distribution with finite support. For a system with a dispatcher and several heterogeneous servers, we propose an optimized multi-layered round robin routing policy followed by shortest remaining processing time scheduling at each server. Using a heavy traffic approximation, we show that the proposed policy performs as well as the optimal scheduling policy for a heterogeneous servers system with a single queue (no routing) in heavy traffic. Additional simulation results suggest that such policies will be effective in more general settings.

Multi-layered round robin routing for parallel servers

We study a system of several identical servers in parallel, where a routing decision must be made immediately on a job’s arrival. Jobs arrive according to a Poisson process, with their processing times following a discrete distribution with finite support. The processing time of a job is known on arrival and may be used in the routing decision. We propose a policy consisting of multi-layered round robin routing followed by shortest remaining processing time scheduling at the servers. This policy is shown to have a heavy traffic limit that is identical to one in which there is a single queue (no routing) and optimal heavy traffic scheduling. In light traffic, we show that the performance of this policy is worse than round robin routing followed by shortest remaining processing time scheduling. We also quantify the difference between round robin and multi-layered round robin routing, which in turn yields insights on the relative importance of routing versus (local) scheduling in such systems.

Generalized load sharing for packet-switching networks. I. Theory and packet-based algorithm

In this paper, we propose a framework to study how to effectively perform load sharing in multipath communication networks. A generalized load sharing (GLS) model has been developed to conceptualize how traffic is split ideally on a set of active paths. A simple traffic splitting algorithm, called packet-by-packet weighted fair routing (PWFR), has been developed to approximate GLS with the given routing weight vector by transmitting each packet as a whole. We have developed some performance bounds for PWFR and found that PWFR is a deterministically fair traffic splitting algorithm. This attractive property is useful in the provision of service with guaranteed performance when multiple paths can be used simultaneously to transmit packets which belong to the same flow. Our simulation studies, based on a collection of Internet backbone traces, reveal that PWFR outperforms two other traffic splitting algorithms, namely, packet-by-packet generalized round robin routing (PGRR), and packet-by-packet probabilistic routing (PPRR).

Generalized load sharing for packet-switching networks. II. Flow-based algorithms

For pt.1 see ibid., p.694-702 (2006). In this paper, we extend the load sharing framework to study how to effectively perform flow-based traffic splitting in multipath communication networks. The generalized load sharing (GLS) model is employed to conceptualize how traffic is split ideally on a set of active paths. A simple flow-based weighted fair routing (WFR) algorithm, called call-by-call WFR (CWFR), has been developed to imitate GLS so that all packets belonging to a single flow are sent on the same path. We have investigated how to couple the proposed basic packet-by-packet WFR (PWFR) and CWFR algorithms so as to permit a traffic splitter to handle both connection-oriented and connectionless traffic simultaneously. Our simulation studies, based on a collection of Internet backbone traces, reveal that WFR outperforms two other traffic splitting algorithms, namely, generalized round robin routing (GRR), and probabilistic routing (PRR). These promising results form a basis for designing future adaptive constraint-based multipath routing protocols.

Optimal Load Balancing on Distributed Homogeneous Unreliable Processors

We consider optimal load balancing in a distributed computing environment consisting of homogeneous unreliable processors. Each processor receives its own sequence of tasks from outside users, some of which can be redirected to the other processors. Processing times are independent and identically distributed with an arbitrary distribution. The arrival sequence of outside tasks to each processor may be arbitrary as long as it is independent of the state of the system. Processors may fail, with arbitrary failure and repair processes that are also independent of the state of the system. The only information available to a processor is the history of its decisions for routing work to other processors, and the arrival times of its own arrival sequence. We prove the optimality of the round-robin policy, in which each processor sends all the tasks that can be redirected to each of the other processors in turn. We show that, among all policies that balance workload, round robin stochastically minimizes the nth task completion time for all n, and minimizes response times and queue lengths in a separable increasing convex sense for the entire system. We also show that if there is a single centralized controller, round-robin is the optimal policy, and a single controller using round-robin routing is better than the optimal distributed system in which each processor routes its own arrivals. Again “optimal” and “better” are in the sense of stochastically minimizing task completion times, and minimizing response time and queue lengths in the separable increasing convex sense.

Optimality of the round-robin routing policy

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.

Optimality of the round-robin routing policy

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.

Algorithms for generalized round robin routing

This paper presents new algorithms to construct a Generalized Round Robin (GRR) routing sequence for distributing one stream of traffic to multiple queues. The performance objective is to minimize the expected delay. Given a target allocation in terms of the fraction of jobs that should be routed to each queue, the algorithms scan the queues in order of descending fraction and assign the next job to the first queue with current allocation not exceeding an easilycomputed threshold. We prove that the constructed sequence has properties related to Hajek's most regular sequence; in particular, it is optimal for the case of two queues. Simulation results show improvement over Itai-Rosberg's Golden Ratio Rule and come very close to a lower bound obtained by Hajek.

Letter to the Editor—A Proof of the Optimality of the Shortest Remaining Processing Time Discipline

Letter to the Editor—A Proof of the Optimality of the Shortest Remaining Processing Time Discipline