All members of the Caltech Microsystems research group provided valuable feedback for the Time Series Prediction study in this thesis. Finally, Pacific Bell provided all the traffic data in this thesis for the Time Series Prediction study, and I am very grateful. We live in an age where computers and computer software are becoming an increasingly integral part of the society in which we live.
Examples of progress are the development of inference theories for expert systems and a better understanding of the capabilities and limitations of neural networks. The benefits of powerful machine learning techniques that can result from this synergy are enormous. Simulations are used to show that there are benefits to be gained from implementing dynamic routing by automating the actions of network managers.
This thesis also examines the application of learning techniques such as neural networks and linear predictors to the tasks of network traffic management. It has been shown that non-linear learning techniques such as neural networks can provide small gains over the more standard technique of linear predictors.
Purpose
Roadmap
- Random Arrivals
- Memoryless Holding Times
- Traffic
- State Diagrams
- State Probabilities
- Erlang Traffic Tables
- Poisson Distribution
- First Routed and Overflow Traffic
- Numerical Example
If all trunks are busy in a trunk group, then no new calls can be accepted in that trunk group. An exception to the assumption of random arrivals is the special case of overflow traffic which. Given N trunks, an arrival rate of X calls per second, and a departure rate of p calls per second, the trunk group state is defined as the number of trunks that are busy in that trunk group.
A state diagram can be drawn to show all the possible states of a group of buses and the rate at which they enter and exit those states. In general, overflow traffic (traffic that has spilled over from the direct path) will not arrive at random moments in time. In other words, an earlier arrival on a bus group carrying excess traffic increases the probability of future arrival.
Define a as the average level of the overflow traffic resulting from random traffic from an Erlangs presented to a stem group of size N. This demonstrates that overflow traffic requires slightly more strains than normal traffic, because it has a greater variation.
Routing Arrangements in Telephone Networks
Hierarchical Routing
Non-Hierarchical Routing
Historical Perspective on Teletraffic Engineering
The seminal paper on telephone network design is a 92-page article by Wilkinson in the 1956 Bell System Technical Journal [Wi156]. This document requires surprisingly little change today when applied to the planning of regional Bell telephone networks. These changes have occurred gradually due to the need to avoid expensive depreciation of the installed network equipment.
Over the coming years, Asynchronous Transfer Mode (ATM) technology can be expected to move from the laboratory to the telephone network. In telephone networks, not enough equipment is provided to enable each customer to establish a simultaneous connection with every other network customer. Traffic measurements are taken and enough equipment is provided in the trunk network to satisfy the expected number of conversations going on at the busiest hour of the day.
Since the network planners are conservative in the amount of equipment installed, it is the job of routing algorithms to ensure that the networks are used efficiently. Dynamic routing algorithms make adjustments to call routing based on the state of the network or based on the time of day.
Dynamic Routing
On the other hand, if there is a lot of traffic between A and B with no traffic originating from either B or C, it can be seen that using the direct route increases the probability that calls from A to B will be blocked, since two-hop calls eliminate termination possibilities. From this simple example it can be seen that a static or dynamic routing algorithm must strike a balance between increasing the efficiency of the global network by performing direct routing whenever possible, and increasing the robustness of the network to failures or patterns. unexpected traffic by offering as many routing options as possible. The first major implementation of dynamic routing in the North American telephone network came with AT&T's implementation of Dynamic Non-Hierarchical Routing (DNHR) which was introduced to the rate network in 1984, with anticipated network savings of 15% [HSS87] .
DNHR is a routing scheme that updates the routing tables depending on time of day. This way, the difference in the busy hours in the different time zones across the US can be taken advantage of. DR5 or dynamic rerouting based on 5-minute data from Bellcore DCR or dynamically controlled rerouting from prism systems.
Description of RTNR
AT&T Network
The network switches are spread across the United States, which means there should be potential savings by taking advantage of the different time zones in the different states.
Signaling System No . 7
If this fails, the switch will make another attempt when the new status information arrives.
Benefits of RTNR
Description of DR5
Regional Bell Telephone Networks
Instead, DR5 takes the approach of using the existing network management infrastructure and adapting it to provide a limited form of dynamic routing. Existing network management capability in the local telephone network allows network administrators to obtain data about each trunk group in the network at 5-minute intervals. If network administrators find a problem in the network, they can perform comprehensive or restrictive controls to redirect traffic or cut down traffic entering the network.
DR5 uses the same interface to network management systems as network operators, calculates redirects based on data from the main channel, and implements these redirects using network management controls. Using simulations, Bellcore has estimated that this approach can provide 50% of the potential benefits of full dynamic routing [CKPSl].
Limitations of DR5
Description of DCR
Expansive Controls
Each switch reports to the network processor every 10 seconds about trunking status, overflow traffic and CPU utilization [Car89]. Using this information, the network processor updates the routing tables of the switches within 5 seconds.
Restrictive Controls
Description of NOAA Dynamic Routing Possibilities
Comparison
Local Versus Global Knowledge
Update Times
Analysis of Dynamic Routing
The network blocking is a function of the blocking on the direct route and the blocking on the alternative route(s). The independence assumption means that the blocking on the direct route is independent of the blocking on the alternative route. The denominator represents the probability that j trunks are busy on leg 1 of the alternate route.
The Bayes estimator is E(Olx), the expected value of the unknown parameter 0 given an observation x. This chapter discusses a number of methods for time series forecasting of occupancy statistics. It is possible that the neural network constructs a Taylor series whose function needs to be approximated.
In contrast, the neural network model is more attractive, requiring a much smaller amount of information to be stored (i.e. weights) to characterize the function to be estimated. Heteroskedasticity is the change in the variance of the occupancy statistic as the level of traffic increases. In this chapter, the dependence of residence on the day of the week is examined.
It is possible to generate a simulated data set using the model of the occupancy process developed in this chapter. It provides a display to the network operators of the state of trunk groups in the network.
Occupancy Dataset
Autocorrelation of (First Order Difference of) Occupancy
Simulation of 36 Erlangs of Traffic
The first step in testing a method is to divide the provided dataset into a test set and a training set. The training set is used to derive the coefficients of the model and the model is then tested on the test set. This maximizes the use of the dataset and allows us to check the significance of the results.
These estimates minimize the sum of the squares of the residuals with respect to the regression parameters. The analysis of correlation coefficients of the data is shown to be an important step in choosing an appropriate model. A plot of hidden unit activations gives valuable insight into the characteristics of the data set.
One of the devices reacts strongly to the speed of change of traffic level, while it. The architecture of the recurrent neural network is somewhat different from the architecture of the other models in this chapter. Then train a linear predictor on that subset of the training set and use it for prediction.
The details of the algorithm used and the best weights to use are given in [Ros87]. The HMM has a side effect of providing a classification of the state of the stem group. In the past, the Monday after Thanksgiving has been found to be the busiest day of the year for phone traffic.
The aim of the model is to explicitly include all the sources of variation in the occupancy readings. By using a long data set with about 18,000 elements, it is possible to have confidence in the comparative performance of the different predict ion techniques. In this way, the significance of the difference in performance between the different prediction methods can be assessed.
Both of these figures assume that the occupation process model is an accurate description of the process. Here, C must be one of the 6 tandem exchanges, due to the hierarchical nature of the network.
Activation of Hidden Unit #3
Activation of Hidden Unit #4
Recurrent Neural Network (Cell Threshold Weights not Shown)
Minimum Error for Local Approximation
Hidden Markov Model State
Hidden Markov Model
Training a Dual Linear Predictor
Comparison of Log and Linear Coefficients
Typical Log Predictions and Linear Predictions . Note that Log and Linear
Wednesday Occupancy Moving Average
Thursday Occupancy Moving Average
Tuesday to Thursday Occupancy Moving Average
Daily Traffic Profile (Tue-Thu)
Traffic Upper and Lower Bounds with Variance(1)
