The games of timing theory enforcing optimal timing intervals and two optimal strategies will be expressed as the following two software theory generated protocols. The two optimal strategy software protocols are first, the battle manager must optimally allocate sensor and weapon systems with the threat launch events. This Internal Battle Manager Decision Optimization(BMDO) Protocol requires the threat constraints of (1) perceived threat inventory, (2) threat missile, and (3) ground asset being attacked. The theoretical generation of the games of timing optimal timing intervals and the two optimal strategies are derived realizing risk management equations within the BMDO Protocol optimization constraints solutions. Invariant Imbedding is the mathematical concept required to contain the BMDO Protocol within the Kernel of the games of timing optimal strategy and optimal timing interval solution to achieve the second and final optimal strategy protocol, the Optimal Battle Manager Decision(OBMD) Protocol. The performance analysis of the OBMD Protocol for constraints and requirements on processor capability and timeliness on a Network Centric Star Topology Architecture is also described for the two Models, Model 1 Mid-course Engagement scenario, and Model 2 Ascent Phase in the Target Trajectory.

The correlated biochemistry and electrical-engineering-based development of the entropy theory is formalized for the parametrization of path information, i.e. storage measures. Similarly, the computer and neural network path delays are developed. Both path parameters are illustrated for the computer networking topological representation of two neural function organs and their interconnection, i.e. the star, the hippocampus computer network representation, and the wheel with a hub, the cerebellum computer network representation. The information measures illustrate the topologically motivated data-compression and connectivity differences. The following computer networking issues are realized in the topological neural network conversion to a functional computer network derivation of path delay and storage parameters: load, real-time requests for various topological structures, concurrency in centralized and distributed networks, deadlock and livelock control, and contention resolution. Category theory is utilized as the mathematical formulation for the definition of simulation in this software theory

The Integrated Services Digital Network (ISDN) provides basic architecture for existing, as well as future residential plus business communications. ISDN overlayed with CCS#7 of a digital PSTN (Public Switched Telephone Network) can be the ultimate, ubiquitous network for circuit switch (voice, data), packet switch (voice, data), and private line (voice, data) applications. Assuming that the present ISDN has to interwork in the present physically separate overlayed networks (voice and data), significant problems are expected to emerge for designing hardware and linking softwares for handling packet traffic. In this paper, the software-related problems, when ISDN packet distribution nodes have to handle an ISDN interface, will be outlined with an ISDN software protocol solution. An approximation of the delay involved in the telephone switching system which is part of ISDN processing as well as the delay for the interface gateways, the HOST computer nodes, and the LAN and WAN computer nodes will be identified and formulated to reflect the total performance measure defined. Major emphasis is given to flow and congestion control performance measures in the ISDN Gateways, which are analyzed and simulated with the assistance of the basic delay table transfer software model developed for the IMPS and gateways in the ARPANET, MILNET, and MINET. The performance evaluation of this basic ISDN interfacing software, which only involved one ISDN level, i.e., the HOST or gateway and its related subnetworks, is simulated on sections of these networks to illustrate its congestion control effectiveness. There are six mathematical software techniques to account for end-to-end delay, which form the basis for the solution to these ISDN software-hardware problems in the Interface Gateways connecting the electronic switch to the computer network components.

A comparison of the performance of the Dynamic Congestion Table (DCT) Algorithm, a computer network congestion control algorithm's delay table entry generation subalgorithm, is made here with a Pascal implementation of the present ARPANET SPF Algorithm (infinite buffer). The parameters of global throughput, delay, and power versus load are evaluated for 10 and 20 node sections of the ARPANET, using M/M/1 service and imterarrival distributions for the computer node (IMP) buffer to obtain computer node mean waiting time. The communication processor and channel delays are determined by the respective probabilistically weighted computer node mean waiting time. Point to point message path delays in the computer network are modeled by the repetitive occurrence of these three component delays in each path. The mathematical structure of two Moore Probabilistic Automatons (MPA) represents the three basic computer network component delays in each path. The probability values of the entries of each of the component MPA are converted to delay entries by the queueing theory node buffer delay computation. The end to end path delay is obtained from a cascaded MPA probability transition matrix, i.e., the multiplication of the individual computer network component MPA matrices. The DCT Algorithm is topology independent and therefore applicable to all centralized and distributed store and forward computer networks. The results indicate higher global throughput and lower global delay for a given load, and significant storage reduction using the DCT Algorithm computation compared to the current ARPANET SPF routing algorithm delay measurement technique.

A new approximation model for the analysis of a finite buffer GI/G/1 system is presented. The approach consists of formulating the computer node mean waiting time from a discrete time marginal overflow customer per time slot solution of a continuous marginal overflow time per customer solution. The key to the model solution is the quantization of the distribution (fu(u)) of the difference between customer service time and customer interarrival time to obtain areas of sections (quantiles) of this probability density function. These quantiles represent the entries of the probability transition matrix of the change in the number of customers allowed in the queue. Irreducible Markov chains represent these uniform quantization lower and upper bound steady state buffer occupancy solutions for the number of customers in the queue at time slot j. A guideline for selecting the optimal quantization interval width is the numerical relation observed between the optimal range of Peak Measurement Accuracy and Peak Measurement Complexity for finite areas of fu(u).

The neural path probabilistic delay (NPPD) algorithm models the neural network in a discrete-time manner analogous to the computer network. The four stages of the basic neuron cell component, i.e. neuron cell body, axon branches, synapse region, and dendrite trees are represented by the mathematical structures of cascaded Markov chains. A state probability transition matrix for the neuron cell is generated by a queueing model of signal interarrival and service rate probability density function (PDF) data. To obtain the delay value for the soma, the PDF functions respectively describing the rate of action potential generation at each cell body and neuron signal arrival at synaptic dendrite terminals, are subtracted and quantized horizontally. This quantization of service minus interarrival PDFs is analogous to the human nervous system encoding of action potential pulses. The specific state transition probability matrices associated with the axon, synapse, and dendrite stages are computed from experimental link structure data. Both PDF and link structure data are measured from neurons located in the specific section of the nervous system considered. An example of the NPPD measure is derived for a neural path in a segment of the cerebellar folium in the cerebellar cortex of the human brain, because a path in this area is initiated by a pain sensation stimulus to the cerebral cortex. Therefore, the motor response path delay parameters for the pain stimulus are of interest in the implementation of the robotic system.

Corporate planning for the automated office requires an increasing awareness of productivity improvement offered by control of office costs. A model for analyzing the cost tradeoffs involved in adding terminals to the communication channels of a local, centralized store and forward computer network for facsimile, data, and/or voice packet switched transmission is presented. The overall cost-benefit analysis is comprised of the three models: customer requirements, network constraints and cost-benefit. The customer requirements model contains six submodels, i.e. load, processor, software, support, terminal, and telecommunications. The network constrains model is composed of the following submodels: computer node submodel, channel submodel, and terminal submodel. The cost-benefit model computes costs for links, terminals, message transactions, and their related cost-benefit ratio, given the final inputs from the network constraints model.