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. Mathematics Subject Classification: primary: 60K25. secondary: 49K30, 49N30, 68M20, 90B22, 90B80. Keywords: Optimal Routing, Scheduling, Sample Path Analysis, Stochastic Ordering. This work was supported in part by the National Science Foundation under grant ASC 88-8802764 and NCR-9116183. y The work of this author was also partially supported by CEC DG-XIII under the ESPRIT-BRA grant QMIPS. 1 Introduction Consider a stream of customers arriving to a controller which immedi...

Scheduling and load balancing for parallel applications can be done at application level, or at system level. Application level scheduling is less transparent, because it has to be coded into each program, and can lead to contradicting decisions, when the different applications do not know about each other. Therefore, in this paper we focus on system level load balancing. We discuss the special properties of heterogeneous workstation clusters for scheduling parallel applications. A Shortest-Expected-Delay mapping is presented that assigns the processes of a parallel application to "virtually homogeneous " machines, based upon the current load situation. We present simulation results that show, how and when process migration is beneficial in heterogeneous systems. Keywords: workstation clusters; heterogeneous systems; parallel applications; scheduling; mapping; 1 Introduction A parallel application consists of a group of communicating processes which have to be assigned to the proces...

Balancing loads in a multiprocessor or multicomputer system can have a significant impact on performance. In this paper, we model such a system as a heterogeneous multi-server queueing system. We study the behavior of such a system operating under the Minimum Expected Delay (MED) routing policy, i.e., an arriving customer is assigned to the queue which has the minimal expected value of unfinished work. This routing discipline can be viewed as a generalization of the join-the-shortest queue (SQ) discipline for homogeneous servers. There is no closed-form solution for this class of queueing problem. In this paper, we provide a methodology to compute upper and lower bounds on the mean response time of the system. This methodology allows one to tradeoff the tightness of the bounds and computational cost. Applications and numerical examples are presented which show how to use this methodology for deriving performance measures and also illustrating that the excellent accuracy of the computat...

Abstract: We consider queueing systems with multiple classes of customers and heterogeneous servers where customers have the flexibility of being processed by more than one server and servers possess the capability of processing more than one customer class. We provide a unified framework for the modeling and analysis of these systems under arbitrary customer and server flexibility and for a rich set of control policies that includes customer/server-specific priority schemes for server and customer selection. We use our models to generate several insights into the effect of system configuration and control policies. In particular, we examine the relationship between flexibility, control policies and throughput under varying assumptions for

A (customer) contact center is a collection of resources providing an interface between a service provider and its customers. The classical contact center is a call center, containing a collection of service representatives (reps) who talk to customers over the telephone. In a call center, the service reps are supported by quite elaborate information-and-communication-technology (ICT) equipment, such as a private branch exchange (PBX), an interactive voice response (IVR) unit, an automatic call distributor (ACD), a personal computer (PC) and assorted databases. With the rapid growth of e-commerce, contact between the service provider and its customers if often made via e-mail or the Internet instead of by telephone. Thus the general interface between a service provider and its customers is now often called a contact center. The design and management of contact centers is important, and worthy of research, because contact centers comprise a large, growing part of the economy and because they are quite complicated. Classic call centers are complicated because

We investigate in this paper submodular properties of the value function arrizing in complex Dynamic programming (DPs). We consider in particular DPs that include concatenation and linear combinations of standard DP operators, as well as combination of maximizations and minimizations. These DPs have many applications and interpretations, both in stochastic control (and stochastic zero-sum games) as well as in the analysis of (noncontrolled) discrete-event dynamic systems. The submodularity implies the monotonicity of the selectors appearing in the DP equations, which translates, in the context of stochastic control and stochastic games, to monotone optimal policies. Our work is based on the score-space approach of Glasserman and Yao.

We consider the practical problem of task assignment in a server farm, where each arriving job is immediately dispatched to a server in the farm. We look at the benefit of cycle stealing at the point of the dispatcher, where jobs normally destined for one machine may be routed to a di#erent machine if it is idle. The analysis uses a technique which we refer to as dimensionality reduction via busy period transitions. Our analysis is approximate, but can be made as close to exact as desired, and is validated via simulation. Results show that the beneficiaries of the idle cycles can benefit unboundedly, due to an increase in their stability region, while the donors are only slightly penalized. These results still hold even when there is only one donor server and 20 beneficiary servers stealing its idle cycles.

We consider the problem of routing customers to one of two parallel queues. Arrivals are independent of the state of the system but otherwise arbitrary. Assuming that queues have infinite capacities and the service times form a sequence of i.i.d. random variables with Increasing Likelihood Ratio (ILR) distribution, we prove that the Shortest Queue (SQ) policy minimizes various cost functionals related to queue lengths and response times. We give a counterexample which shows that this result is not generally true when the service times have Increasing Hazard Rate but are not increasing in the likelihood rate sense. Finally, we show that when capacities are finite the SQ policy stochastically maximizes the departure process and minimizes the loss counting process. Keywords: Routing; stochastic majorization; response times; increasing likelihood ratio distributions AMS subject classification: 60K25 1 Introduction A classical problem in the literature of control of queues is the determin...

The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov

This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solution methodology.