Abstract

We study how multi-product queueing systems should be controlled so that sojourn times (or end-to-end delays) do not exceed specified leadtimes. The network dynamically decides when to admit new arrivals and how to sequence the jobs in the system. To analyze this difficult problem, we propose an approach based on fluid-model analysis that translates the leadtime specifications into deterministic constraints on the queue length vector. The main benefit of this approach is that it is possible (and relatively easy) to construct scheduling and multi-product admission policies for leadtime control. Additional results are: (a) While this approach is simpler than a heavy-traffic approach, the admission policies that emerge from it are also more specific than, but consistent with, those from heavy-traffic analysis. (b) A simulation study gives a first indication that the policies also perform well in stochastic systems. (c) Our approach specifies a “tailored” admission region for any given sequencing policy. Such joint admission and sequencing control is “robust” in the following sense: system performance is relatively insensitive to the particular choice of sequencing rule when used in conjunction with tailored admission control. As an example, we discuss the tailored admission regions for two well-known sequencing policies: Generalized Processor Sharing and Generalized Longest Queue. (d) While we first focus on the multi-product single server system, we do extend to networks and identify some subtleties.

Author Keywords: Queueing; Scheduling; Lead times; Admission control; Fluid models

Article Outline

1. Introduction

2. The multi-product single server system with leadtime constraints

3. Admission control in the single server system

3.1. The largest transient admission region R_T and GSD sequencing

3.2. Admission control regions tailored to different sequencing rules

3.2.1. Admission region under GLQ(θ)

3.2.2. Admission region under GPS(φ)

3.3. Mixed analysis: Fluid model with batch arrivals

4. Simulation study of the control policies in the stochastic single-server system

4.1. Performance without admission control

4.2. Performance with admission control

5. Multi-class networks with leadtime constraints

5.1. Network model

5.2. Modeling and control for multi-class networks with leadtime constraints

5.3. Admission control in networks with leadtime constraints

5.4. Sequencing in networks with leadtime constraints

6. Concluding remarks

Acknowledgements

Appendix A. Proofs

A.1. Proof of Proposition 2

A.2. Proof of Proposition 3: GLQ(θ) fluid admission region

A.3. Proof of Proposition 5: GPS(φ) fluid admission region

A.4. Proof of Proposition 7

References