Optimal Control Problems In Communication Networks With Information Delays And Quality Of Service Constraints
Joy Kuri · 1995
In this thesis, we consider optimal control problems arising in high-speed integrated communication networks with Quality of Service (QOS) constraints. Integrated networks are expected to carry a large variety of traffic sources with widely varying traffic characteristics and performance requirements. Broadly, the traffic sources fall into two categories: (a) real-time sources with specified performance criteria, like small end to end delay and loss probability (sources of this type are referred to as Type 1 sources below), and (b) sources that do not have stringent performance criteria and do not demand performance guarantees from the network - the so-called Best Effort Type sources (these are referred to as Type 2 sources below). From the network's point of view, Type 2 sources are much more controllable than Type 1 sources, in the sense that the Type 2 sources can be dynamically slowed down, stopped or speeded up depending on traffic congestion in the network, while for Type 1 sources, the only control action available in case of congestion is packet dropping. Carrying sources of both types in the same network concurrently while meeting the performance objectives of Type 1 sources is a challenge and raises the question of equitable sharing of resources. The objective is to carry as much Type 2 traffic as possible without sacrificing the performance requirements of Type 1 traffic. We consider simple models that capture this situation. Consider a network node through which two connections pass, one each of Types 1 and 2. One would like to maximize the throughput of the Type 2 connection while ensuring that the Type 1 connection's performance objectives are met. This can be set up as a constrained optimization problem that, however, is very hard to solve. We introduce a parameter b that represents the of buffer occupancy by Type 2 traffic. Since buffer space is limited and shared, a queued Type 2 packet means that a buffer position is not available for storing a Type 1 packet; to discourage the Type 2 connection from hogging the buffer, the cost parameter b is introduced, while a reward for each Type 2 packet coming into the buffer encourages the Type 2 connection to transmit at a high rate. Using standard on-off models for the Type 1 sources, we show how values can be assigned to the parameter b; the value depends on the characteristics of the Type 1 connection passing through the node, i.e., whether it is a Variable Bit Rate (VBR) video connection or a Continuous Bit Rate (CBR) connection etc. Our approach gives concrete networking significance to the parameter b, which has long been considered as an abstract parameter in reward-penalty formulations of flow control problems (for example, [Stidham '85]). Having seen how to assign values to b, we focus on the Type 2 connection next. Since Type 2 connections do not have strict performance requirements, it is possible to defer transmitting a Type 2 packet, if the conditions downstream so warrant. This leads to the question: what is the best transmission…