Optimal Static Load Balancing Research Articles

Paradoxes in distributed decisions on optimal load balancing for networks of homogeneous computers

In completely symmetric systems that have homogeneous nodes (hosts, computers, or processors) with identical arrival processes, an optimal static load balancing scheme does not involve the forwarding of jobs among nodes. Using an appropriate analytic model of a distributed computer system, we examine the following three decision schemes for load balancing: completely distributed, intermediately distributed, and completely centralized. We show that there is no forwarding of jobs in the completely centralized and completely distributed schemes, but that in an intermediately distributed decision scheme, mutual forwarding of jobs among nodes is possible, leading to degradation in system performance for every decision maker. This result appears paradoxical, because by adding communication capacity to the system for the sharing of jobs between nodes, the overall system performance is degraded. We characterize conditions under which such paradoxical behavior occurs, and we give examples in which the degradation of performance may increase without bound. We show that the degradation reduces and finally disappears in the limit as the intermediately distributed decision scheme tends to a completely distributed one.

Uniqueness of the solution for optimal static routing in open BCMP queueing networks

Optimal static routing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. They include static routing problems in communication networks and optimal static load balancing problems in distributed computer systems. We consider an overall optimal policy that is the routing policy whereby the overall mean response (or sojourn) time of a job is minimized. We obtain the routing decisions of the overall optimal policy and show that they may not be unique, but that the utilization of each service center is uniquely determined by the overall optimal policy. We also consider an individually optimal policy whereby jobs are routed so that each job may feel that its own expected response time is minimized if it knows the mean delay time for each path.

Optimal Static Load Balancing in Star Network Configurations with Two-Way Traffic

We study the static load balancing problem in a distributed computer system that consists of a set of heterogeneous computer systems interconnected by a star network with two-way traffic. We formulate the static load balancing problem as a nonlinear optimization problem which minimizes the mean response time. We prove that in the optimal solution the satellite nodes in the star network can be divided into four different types: the idle source nodes, the active source nodes, the neutral nodes, and the sink nodes. The necessary and sufficient conditions for optimal solution are studied. An efficient algorithm of complexity O(n) is proposed for the static load balancing of an n-satellite system. The effects of link communication time on optimal load balancing in a star network are also studied by parametric analysis. By employing the proposed algorithm, a significant system performance improvement over that without load balancing is illustrated in a numerical example. The numerical example also shows that the effects of the link communication time in a star network are large.

Effects of node processing time on optimal load balancing in tree hierarchy network configurations

In this paper, optimal static load balancing in a tree hierarchy network that consists of a set of heterogeneous host computers is considered. It is formulated as a nonlinear optimization problem. By parametric analysis, we study the effects of the node processing time on the optimal link flow rate (i.e. the rate at which a node forwards jobs to other nodes for remote processing), the optimal node load (i.e. the rate at which jobs are processed at a node), and the optimal mean response time. We show that the entire network can be divided into several independent sub-tree networks with respect to the link flow rates and node loads. We find that the processing time of a node affects only the link flow rates and the loads of nodes which are in the same sub-tree network. Generally, an increase in the processing time of an arbitrary node causes an increase in the link flow rates of its ancestor nodes and itself, but causes a decrease in the link flow rates of its descendant nodes and its collateral nodes in the same sub-tree network. It also causes a decrease in the load of the node itself, but causes an increase in the loads of other nodes in the same sub-tree network. Furthermore, it causes an increase in the mean response time. By conducting numerical experiments, we find that the node processing time possesses a large influence on the system performance measures. Knowledge of the effects of node processing time is useful in designing networks or making a parametric adjustment to improve the system performance.

An algorithm for optimal static load balancing in distributed computer systems

The authors propose a load-balancing algorithm that determines the optimal load for each host so as to minimize the overall mean job response time in a distributed computer system that consists of heterogeneous hosts. The algorithm is a simplified and easily understandable version of the single-point algorithm originally presented by A.N. Tantawi and D. Towsley (1985). >

Optimal static load balancing in distributed computer systems

A distributed computer system that consists of a set of heterogeneous host computers connected in an arbitrary fashion by a communications network is considered. A general model is developed for such a distributed computer system, in which the host computers and the communications network are represented by product-form queuing networks. In this model, a job may be either processed at the host to which it arrives or transferred to another host. In the latter case, a transferred job incurs a communication delay in addition to the queuing delay at the host on which the job is processed. It is assumed that the decision of transferring a job does not depend on the system state, and hence is static in nature. Performance is optimized by determining the load on each host that minimizes the mean job response time. A nonlinear optimization problem is formulated, and the properties of the optimal solution in the special case where the communication delay does not depend on the source-destination pair is shown. Two efficient algorithms that determine the optimal load on each host computer are presented. The first algorithm, called the parametric-study algorithm , generates the optimal solution as a function of the communication time. This algorithm is suited for the study of the effect of the speed of the communications network on the optimal solution. The second algorithm is a single-point algorithm ; it yields the optimal solution for given system parameters. Queuing models of host computers, communications networks, and a numerical example are illustrated.