Abstract

We consider an ingress optical burst switching (OBS) node employing the JumpStart signaling protocol. The switch serves a number of users, each connected to the switch with a fiber link that supports multiple wavelengths. Each wavelength is associated with a 3-state Markovian burst arrival process which permits short and long bursts to be modeled. We model the ingress switch as a closed multi-class non-product-form queueing network, which we analyze approximately by decomposition. Specifically, we develop new techniques to analyze the queueing network, first assuming a single class of customers, and subsequently multiple classes of customers. These analytical techniques have applications to general queueing networks beyond the one studied in this paper. We also develop computationally efficient approximate algorithms to analyze an ingress switch in the limiting case where the number of wavelengths is large. The algorithms have a good accuracy, and they provide insight into the effect of various system parameters on the performance of an ingress OBS switch.

Keywords: Optical burst switching; JumpStart project; Marie’s algorithm; Multi-class queueing networks; Closed non-product-form queueing networks

Article Outline

1. Introduction

2. JumpStart project

2.1. Network architecture

2.2. An ingress switch

3. The burst arrival process

3.1. Related work and motivation

3.2. Description of the burst arrival process

4. A queueing network model of an ingress OBS node

4.1. Ingress OBS node without converters

4.2. Ingress OBS node with converters

5. Analysis of the single-class queueing network without converters

5.1. The flow equivalent server

5.2. The iterative algorithm

6. Analysis of the single-class queueing network with converters

7. Analysis of the multi-class queueing network with or without converters

8. An ingress node with a large number of wavelengths

8.1. Two properties when W is large

9. Numerical results

9.1. Single-class network

9.2. Multi-class network

9.3. A large number of wavelengths

9.3.1. The effect of the traffic load

9.3.2. The effect of the traffic pattern

9.3.3. The effect of the orbiting rate

9.3.4. The effect of different burst arrival processes

10. Complexity of approximate algorithms

11. Concluding remarks

Appendix A. Analysis of the multi-class queueing network with or without converters

A.1. The two-class queueing network

A.2. The iterative algorithm for analyzing more than two classes

A.2.1. Class aggregation

A.2.2. The iterative algorithm

Appendix B. An ingress node with a large number of wavelengths

B.1. Analysis of the single-class queueing network when W is large

B.1.1. The conditional throughput

B.1.2. The iterative algorithm

B.1.3. The mean waiting time

B.2. Analysis of the multi-class queueing network when W is large

B.2.1. Class aggregation

B.2.2. The iterative algorithm

References

Vitae

This work was supported by the Intelligence Technology Innovation Center under contract MDA904-00-C-2133.