Flavio Bonomi

Adaptive optimal load balancing in a nonhomogeneous multiserver system with a central job scheduler

A model comprising several servers, each equipped with its own queue and with possibly different service speeds, is considered. Each server receives a dedicated arrival stream of jobs; there is also a stream of generic jobs that arrive to a job scheduler and can be individually allocated to any of the servers. It is shown that if the arrival streams are all Poisson and all jobs have the same exponentially distributed service requirements, the probabilistic splitting of the generic stream that minimizes the average job response time is such that it balances the server idle times in a weighted least-squares sense, where the weighting coefficients are related to the service speeds of the servers. The corresponding result holds for nonexponentially distributed service times if the service speeds are all equal. This result is used to develop adaptive quasi-static algorithms for allocating jobs in the generic arrival stream when the load parameters are unknown. The algorithms utilize server idle-time measurements which are sent periodically to the central job scheduler. A model is developed for these measurements, and the result mentioned is used to cast the problem into one of finding a projection of the root of an affine function, when only noisy values of the function can be observed. >

An approximate analysis for a class of assembly-like queues

Assembly-like queues model assembly operations where separate input processes deliver different types of component (customer) and the service station assembles (serves) these input requests only when the correct mix of components (customers) is present at the input. In this work, we develop an effective approximate analytical solution for an assembly-like queueing system withN(N ⩾ 2) classes of customers formingN independent Poisson arrival streams with rates {λi=1,...,N} The arrival of a class of customers is “turned off” whenever the number of customers of that class in the system exceeds the number for any of the other classes by a certain amount. The approximation is based on the decomposition of the originalN input stream stage into a cascade ofN-1 two-input stream stages. This allows one to refer to the theory of paired customer systems as a foundation of the analysis, and makes the problem computationally tractable. Performance measures such as server utilization, throughput, average delays, etc., can then be easily computed. For illustrative purposes, the theory and techniques presented are applied to the approximate analysis of a system withN = 3. Numerical examples show that the approximation is very accurate over a wide range of parameters of interest.

Adaptive optimal load balancing in a heterogeneous multiserver system with a central job scheduler

The authors formally state and discuss the response time minimization problem. They show the equivalence of this problem to a weighted least square load balancing problem. They also discuss the correct solution of these problems. Next they describe and analyze a class of server idle time measurements. Finally, a class of adaptive algorithms is presented, and their performance is studied via simulation experiments.<<ETX>>

On job assignment for a parallel system of processor sharing queues

Two of the optimality criteria most commonly considered to compare job assignment policies, namely, the stochastic order and the average total completion time criterion, are discussed. It is shown that the latter, while being weaker than the former, still provides a useful criterion when policies are to be evaluated in terms of average performance measures such as the system average response time. Some of the most relevant results available in the literature on job assignment to parallel first come, first served (FCFS) servers are summarized. The assignment problem is discussed for a parallel system of processor sharing (PS) queues with exponential interarrival times and exponential and identical service requirements. The optimality of the join-the-shortcut-queue (JSQ) assignment policy for this case is proven. Feasible policies for general service time distribution are discussed. An approach allowing a meaningful comparison of servers in the perspective of job assignment is proposed. A comparison of the assignment problem for FCFS and PS parallel systems is presented. >

Busy period analysis for an ATM switching element output line

The authors consider an N*N asynchronous transfer mode (ATM) switching element with output queuing, under a uniformity assumption for the traffic arriving on the various input lines and for the output line address of the incoming cells. The traffic on each input line is modeled as a two-state Markov chain. The distribution of the busy and idle periods for each output line is analytically derived. It is concluded that it is not easy to identify a simple two-state Markov chain model that provides an adequate description for the output traffic. The implications of two different output line address assignment mechanisms for the incoming cells are quantitatively described. An alternative method is outlined for the computation of the steady-state distribution of the number of cells in the system. An analysis of the numerical results is presented.<<ETX>>

Public computer systems—a challenge for organizational learning

Statistical multiplexing is one of the core techniques behind the concept of Broadband Integrated Services Digital Networks based on ATM. In this paper we study a model of a statistical multiplexer with non-homogeneous bursty traffic, in order to investigate its transient and steady state behavior, and to characterize the nature of its output traffic. Our study represents an effort wo widen our perspective on the advantages and pitfalls of statistical multiplexing, by considering a set of issues not yet deeply covered in the available literature. Our overall conclusions indicate that the full advantages promised by statistical multiplexing in the context of ATM networks cannot be obtained without careful discrimination and new and innovative approaches to access and congestion control. In particular, our results suggest using statistical multiplexing closer to the edges of the network, when many lower speed sources can be multiplexed; offering separated treatment to widely different types of traffic; and considering alternative methods of access control for particular services, such as long file transfers. K~Twords: queueing systems; ATM networks; statistical multiplexing; transient analysis; mathematical modeling.The ‘Electronic Highway’ is most often discussed as a network of computers and cables, but it is also a service infrastructure and as a new communication medium bringing individuals and organizations together in new ways. Public Computer Systems (PCS), computers employed as an interface between organizations and their clients, are discussed as actors in client-organization relations in terms of the nature of the service delivered, the focus in terms of activities in the business process, role changes on part of professionals and clients, and the communicational style of the systems. It is concluded that PCS are not just information delivery machines, but also actors in a dialogue. Different designs of PCS will lead to the action space on part of the human actors changing in different ways.

An adaptive join-the-biased-queue rule for load sharing on distributed computer systems

An adaptive version of the join-the-biased-queue rule, originally proposed for the assignment of jobs to a simple parallel system of queues, is presented. The adaptive algorithm provides the foundation for an adaptive load sharing routine for a class of Unix multiprocessor systems. The authors utilize a combination of the available instantaneous information about the number of processes active on each processor and periodically collected average CPU run-queue-length information as an index of load to aid in assigning processes to the various processors for execution. Their algorithm aims at maintaining the system in an operating condition characterized by a balance in the normalized average CPU run-queue-lengths observed by the various processors, even when the offered workload has unknown and time-varying characteristics. The bias components in the join-the-biased-queue rule are periodically recalculated by using a simple stochastic approximation procedure. The load sharing strategy consistently deals with the constraints imposed by the nature of the considered systems and their workload, such as overheads and implementation costs, nonhomogeneities, measurement errors, and nonmigration. Extensive simulation studies of the algorithm behavior, together with laboratory measurements on the algorithm implementation for the AT&T 3B4000 computer system, confirm the superior performance, stability, and robustness of the algorithm. The approach can be applied in the solution of load sharing or routing problems in more general contexts than the one considered.<<ETX>>

Optimality of weighted least squares load balancing

The authors consider a model comprising several servers, with possibly different services speeds, each equipped with its own queue. Each server receives a dedicated arrival stream of jobs; there is also a stream of generic jobs that arrive at a job scheduler and can be individually allocated to any of the servers. It is shown that if the arrival streams are all Poisson, and all jobs have the same exponentially distributed service requirements, then the probabilistic splitting of the generic stream that minimizes the average job response time is one that balances the server idle times in a weighted least squares sense, where the weighting coefficients are related to the service speeds of the servers. The corresponding result holds for nonexponentially distributed service times, if the service speeds are all equal.<<ETX>>

Flow control for the ATM available bit rate service

During the past year the identification of appropriate flow control mechanisms for the support of the new available bit rate (ABR) ATM service has attracted the intense interest of the technical community worldwide. A key aspect of the ABR service definition is the reliance an a feedback control loop linking the potential points of congestion in an ATM network and the sources of data. The feedback control of the flow of data cells within multiservice networks characterized by both extremely high data rates, and possibly long propagation delays poses formidable challenges. This is particularly true when very strict quality of service requirements are imposed, together with the need to reduce expensive buffering needs. In this paper the author discusses some fundamental and sometimes new control aspects brought to the surface by the intense effort towards the definition of appropriate feedback flow control schemes for the ABR service. The primary goal for the ABR service is the economical support of applications with vague requirements for throughputs and delays.

An Adaptive Regulator Approach for the Design of Load Sharing Algorithms

In this work we presented a novel approach to the design of load sharing algorithms for a class of multiprocessor systems. This approach was used in the definition of an adaptive load balancing algorithm, which we call AJBQ, which is successfully implemented on the AT&T 3B4000 UNIX® multiprocessor. The algorithm led to a significant improvement in system performance with a very small overhead, and has been designed to take advantage of software and hardware mechanisms available on the system. The adaptive (i.e., learning) properties of the proposed procedure offer advantages in terms of ability to react to sudden changes in the system configuration and workload, reduced hand-tuning requirements, and robustness with respect to workload/configuration combinations.