Congestion in a queueing system can sometimes be controlled by restricting arrivals, either by "closing a gate" or by charging an entrance fee or toll. We review both static (open-loop) and dynamic (closed-loop) models for control of admission to a queueing system. The main emphases are on the difference between socially optimal and individually optimal (equilibrium) controls and on the use of dynamic-programming inductive analysis to show that an optimal control is monotonic or characterized by one or more "critical numbers." We discuss the potential for use of these models in the analysis of computer/ communication systems and compare the results to certain others in the literature.

Optimal control of admission to a queueing system

In this paper we describe briefly a dynamic multi-path routing scheme that has been considered for connection oriented homogeneous high speed networks. The fundamental objective of the scheme is to bridge the gap between routing and congestion control as the network becomes congested. Because propagation delay far out shadows queueing and transmission delay in high speed networks, the proposed routing scheme works as a shortest path (minimum hop) first algorithm under light traffic conditions. However as the shortest path becomes congested, the source node uses multiple paths when and if available in order to distribute the load and reduce packet loss. The scheme is a cross between Alternate Path routing and Trunk Reservation.We compare the performance of the proposed scheme with the Shortest Path Only algorithm, the Alternate Path routing algorithm, the Random Routing algorithm, and the Trunk Reservation scheme. The throughput and packet loss performance are compared via simulations. These have been carried out concentrating on a 5 node network with varying traffic patterns, the intention being to gain insight into the strengths and weaknesses of the various schemes.

Dynamic multi-path routing and how it compares with other dynamic routing algorithms for high speed wide area network

This paper focuses on network delays as they apply to voice traffic. First the nature of the delay problem is discussed and this is followed by a review of enhanced circuit, packet, and hybrid switching techniques: these include fast circuit switching (FCS), virtual circuit switching (VCS), buffered speech interpolation (SI), packetized virtual circuit (PVC), cut-through switching (CTS), composite packets, and various frame management strategies for hybrid switching. In particular, the concept of introducing delay to resolve contention in SI is emphasized, and when applied to both voice talkspurts and data messages, forms a basis for a relatively new approach to network design called transparent message switching (TMS). This approach and its potential performance advantages are reviewed in terms of packet structure, multiplexing scheme, network topology, and network protocols. The paper then deals more specifically with the impact of variable delays on voice traffic. In this regard the importance of generating and preserving appropriate length speech talkspurts in order to mitigate the effects of variable network delay is emphasized. The results indicate that a desirable length of talkspurt "hangover" of about 200 ms will accomplish this without unduly affecting speech activity, and that, under these circumstances, the perceptable threshold of variable talkspurt delay can be as high as about 200 ms average. As such, the results provide a useful guideline for integrated services system designers. Finally, suggestions are made for further studies on performance analysis and subjective evaluation of advanced integrated services systems.

Delay Related Issues in Integrated Voice and Data Networks

An efficient and flexible algorithm is presented for finding a k shortest loopless path with distinct initial links from one node to each other node. Low-order polynomial bounds are established for the worst-case time complexity of the algorithm, showing it to offer a substantial improvement over applying known algorithms to the problem. The algorithm can incorporate various extensions, including the ability to handle an algebraic objective, which enhance its applicability to diverse network models. In addition, the k shortest path formulation and algorithm are proposed as a basis for network survivability measures where path length bounds exist. >

A k shortest path algorithm for adaptive routing in communications networks

A K-Shortest Path Algorithm for Adaptive Routing in Communication Networks.

This is an expanded version of an earlier report, adding, new results. The first part introduces a simple analytic model showing that dynamic routing may increase network throughput or lower delay when trunks are moderately loaded, but will reduce throughput or increase delay at heavy trunk loads. The second part of the paper presents simulation results characterizing: 1) the operation of a network "protected" by end-to-end flow control, 2) the operation of an "unprotected" network, 3) the transition between these two modes, 4) the effect of changing the update interval for the routing algorithms, 5) the effect of slow local loops, and 6) the effect of increasing the number of alternate paths available for dynamic routing. Overall, the results show that dynamic routing improves network performance only over a small parameter range, and should dynamic routing be used at all, it must be implemented with great care.

Dynamic Routing and Flow Control

In the field of communications, an ever-increasing number of system functions is realized in digital form. In this context, the problem of economical analog/digital conversion becomes an important issue. The cost of analog/digital conversion, however, is often dominated by the associated filters required for the prevention of foldover distortion. For this reason, an approach characterized by analog filtering (with relaxed requirements) before A/D conversion, and additional, digital, time-shared filtering after A/D conversion, becomes an attractive solution. In this paper, the signal-to-noise ratio of such a system is analyzed. The analysis includes quantization noise and overload distortion from the analog/digital conversion process, additional noise due to codec imperfections and round-off noise from the digital filters and interpolators. A design example, that was also implemented in hardware, demonstrates that the specifications of the CCITT can be easily met.

H. Mueller

Papers

Dynamic Routing and Flow Control

Signal-to-Noise Analysis of a PCM Voice System Based on Analog/Digital Filtering