Incentive effects of common and separate queues with multiple servers: The principal-agent perspective

A two-server service network has been studied by Gilbert and Weng [13] fromthe principal-agent perspective. In the model, services are rendered by twoindependent facilities coordinated by an agency. The agency must devise astrategy to allocate customers to the facilities and determine the compensation.A common queue allocation scheme and separate queue allocation scheme are thencompared. It has been shown that the separate queue system gives morecompetition incentives to the independent facilities and induces a higherservice capacity. The main aim of this paper is to extend the results of thetwo-server queueing model to the case of multiple-server queueing model. Ouranalysis shows that in the case of multiple servers the separate queueallocation scheme creates more competition incentives for servers to increasetheir service capacities. In particular, when there are not severe diseconomiesassociated with increasing service capacity, the separate queue allocationscheme gives a lower expected sojourn time in equilibrium. © 2009 IEEE.published_or_final_versionProceedings of the 39th International Conference on Computers and Industrial Engineering (CIE39), Troyes, France, 6-8 July 2009, p. 1249-125

Asymptotically Optimal Size-Interval Task Assignments

International audienceSize-based routing provides robust strategies to improve the performance of computer and communication systems with highly variable workloads because it is able to isolate small jobs from large ones in a static manner. The basic idea is that each server is assigned all jobs whose sizes belong to a distinct and continuous interval. In the literature, dispatching rules of this type are referred to as SITA (Size Interval Task Assignment) policies. Though their evident benefits, the problem of finding a SITA policy that minimizes the overall mean (steady-state) waiting time is known to be intractable. In particular it is not clear when it is preferable to balance or unbalance server loads and, in the latter case, how. In this paper, we provide an answer to these questions in the celebrated limiting regime where the system capacity grows linearly with the system demand to infinity. Within this framework, we prove that the minimum mean waiting time achievable by a SITA policy necessarily converges to the mean waiting time achieved by SITA-E, the SITA policy that equalizes server loads, provided that servers are homogeneous. However, within the set of SITA policies we also show that SITA-E can perform arbitrarily bad if servers are heterogeneous. In this case we prove that there exist exactly C! asymptotically optimal policies, where C denotes the number of server types, and all of them are linked to the solution of a single strictly convex optimization problem. It turns out that the mean waiting time achieved by any of such asymptotically optimal policies does not depend on how job-size intervals are mapped to servers. Our theoretical results are validated by numerical simulations with respect to realistic parameters and suggest that the above insights are also accurate in small systems composed of a few servers, i.e., ten

Load Balancing with Job-Size Testing: Performance Improvement or Degradation?

In the context of decision making under explorable uncertainty, scheduling with testing is a powerful technique used in the management of computer systems to improve performance via better job-dispatching decisions. Upon job arrival, a scheduler may run some \emph{testing algorithm} against the job to extract some information about its structure, e.g., its size, and properly classify it. The acquisition of such knowledge comes with a cost because the testing algorithm delays the dispatching decisions, though this is under control. In this paper, we analyze the impact of such extra cost in a load balancing setting by investigating the following questions: does it really pay off to test jobs? If so, under which conditions? Under mild assumptions connecting the information extracted by the testing algorithm in relationship with its running time, we show that whether scheduling with testing brings a performance degradation or improvement strongly depends on the traffic conditions, system size and the coefficient of variation of job sizes. Thus, the general answer to the above questions is non-trivial and some care should be considered when deploying a testing policy. Our results are achieved by proposing a load balancing model for scheduling with testing that we analyze in two limiting regimes. When the number of servers grows to infinity in proportion to the network demand, we show that job-size testing actually degrades performance unless short jobs can be predicted reliably almost instantaneously and the network load is sufficiently high. When the coefficient of variation of job sizes grows to infinity, we construct testing policies inducing an arbitrarily large performance gain with respect to running jobs untested

Allocation of Service Time in a Multiserver System

Reducing congestion is a primary concern in the design and analysis of queueing networks, especially in systems where sources of randomness are characterized by high variability. This paper considers a multiserver first-come, first-served (FCFS) queueing model where we arrange servers in two stations in series. All arrivals join the first service center, where they receive a maximum of T units of service. Arrivals with service requirements that exceed the threshold T join the second queue, where they receive their remaining service. For a variety of heavy tail service time distributions, characterized by large coefficient of variations, analytical and numerical comparisons show that our scheme provides better system performance than the standard parallel multiserver model in the sense of reducing the mean delay per customer in heavy traffic systems. Our model is likely to be useful in systems where high variability is a cause for degradation and where numerous service interruptions are not desired.queueing, truncated distributions, heavy tail distributions, repair models, simulation