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NASA NTRS1989

Queuing theory models for computer networks

A set of simple queuing theory models which can model the average response of a network of computers to a given traffic load has been implemented using a spreadsheet. The impact of variations in traffic patterns and intensities, channel capacities, and message protocols can be assessed using them because of the lack of fine detail in the network traffic rates, traffic patterns, and the hardware used to implement the networks. A sample use of the models applied to a realistic problem is included in appendix A. Appendix B provides a glossary of terms used in this paper. This Ames Research Center computer communication network is an evolving network of local area networks (LANs) connected via gateways and high-speed backbone communication channels. Intelligent planning of expansion and improvement requires understanding the behavior of the individual LANs as well as the collection of networks as a whole.

Galant, David C.↗

DOE OSTI2024

Balancing Charging Station Utilization and Throughput in Electric Vehicle Charging Stations with Queuing Theory

The rapid increase in electric vehicle (EV) adoption demands enhancements in the efficiency and adaptability of EV supply equipment (EVSE). Traditional EVSE systems often fail to optimize power delivery to meet the variable acceptance rates of EV batteries, resulting in significant energy wastage and reduced operational efficiency. This research addresses these challenges by integrating queuing theory with modular EVSE architectures, offering a dual strategy to optimize the operation of EV charging stations. A simulation model was developed to assess various configurations of charger capacities and outlet numbers. This model aimed to identify the optimal setup that maximizes station utilization while minimizing charging times and maximizing throughput. The model focused on charger capacities ranging from 50 to 250 kW and analyzed the different capacities’ effects on charging times and the number of vehicles served. The results indicate that a charger capacity of 125 kW is optimal, striking a balance between the charging time and the number of EVs served per hour, thus achieving the highest station utilization rate. This capacity allows for servicing a significant number of EVs with moderate increases in charging times. Lower capacities, although capable of serving more vehicles, lead to longer charging times and decreased throughput efficiency. The study underscores the effectiveness of combining queuing theory with flexible, modular charging systems that can dynamically adjust to EV charging demands.

Kumar, Praveen↗

NASA NTRSDate not supplied

A Queuing Theory Approach to Pilot-Controller Coordination for m:N Operations

In recent years, attention and interest by industry and researchers has grown in a control paradigm for remotely piloted aircraft termed “m:N operations.” In an m:N operation, a team of m remote pilots in command (RIPCs) collaboratively manage the flights of N aircraft. A consequence of an m:N concept of operations is that the RPICs will have to switch attention from one aircraft to another and from one task to another. Previous research in m:N operations has focused on the workload experienced by an RPIC and their level of situation awareness on their flights. Researchers have found that RPIC workload and situation awareness are generally sensitive to increasing N, although NASA’s Multi-Vehicle (m:N) Working Group has suggested that the driver of workload/situation awareness is the number of exceptions requiring human intervention as opposed to the value of N itself. In any case, a natural antecedent of workload is task load. In this paper, queueing theory is applied to a 1:N Urban Air Mobility (UAM) air taxi operation in order to estimate pilot task load for managing radio communications with air traffic controllers (ATCs) under increasing N. An M/M/1 queueing system is used to model the RIPC’s servicing of calls and clearance requests (e.g., departure, arrival, or airspace transition) to ATC for the N aircraft. Important parameters for the queueing model are the task arrival rate and the average service time for task completion. Radio communication times from past human-in-the-loop simulation studies are used to measure service times for a 1:4 and 1:12 UAM operation and to interpolate service times for 4 < N < 12. A Monte Carlo method is then employed, using the measured and interpolated service times, to estimate arrival rate and related queueing statistics. The paper concludes by considering the estimated queuing statistics, particularly the RPIC’s utilization (i.e., proportion of time actively servicing tasks), the length of the task queue over time, and the implications for task-balanced system design.

task load↗

NASA NTRS1972

Job-mix modeling and system analysis of an aerospace multiprocessor.

An aerospace guidance computer organization, consisting of multiple processors and memory units attached to a central time-multiplexed data bus, is described. A job mix for this type of computer is obtained by analysis of Apollo mission programs. Multiprocessor performance is then analyzed using: 1) queuing theory, under certain 'limiting case' assumptions; 2) Markov process methods; and 3) system simulation. Results of the analyses indicate: 1) Markov process analysis is a useful and efficient predictor of simulation results; 2) efficient job execution is not seriously impaired even when the system is so overloaded that new jobs are inordinately delayed in starting; 3) job scheduling is significant in determining system performance; and 4) a system having many slow processors may or may not perform better than a system of equal power having few fast processors, but will not perform significantly worse.

Mallach, E. G.↗

NASA NTRS1976

Simulating an aerospace multiprocessor

The paper describes a simulator which was used to evaluate the architecture of an aerospace multiprocessor. The simulator models interactions among the processors, memories, the central data bus, and a possible 'job stack'. Special features of the simulator are discussed, including the use of explicitly coded and individually distinguishable 'job models' instead of a statistically defined 'job mix' and a specialized Job Model Definition Language to automate the detailed coding of the models. Some results are presented which show that when the simulator was employed in conjunction with queuing theory and Markov-process analysis, more insight into system behavior was obtained than would have been with any one technique alone.

Mallach, E. G.↗

NASA NTRS1992

Spreadsheet Analysis Of Queuing In A Computer Network

Method of analyzing responses of computer network based on simple queuing-theory mathmatical models via spreadsheet program. Effects of variations in traffic, capacities of channels, and message protocols assessed.

Galant, David C.↗

NASA NTRS1991

Applying generalized stochastic Petri nets to manufacturing systems containing nonexponential transition functions

Generalized stochastic Petri nets (GSPNs) are applied to flexible manufacturing systems (FMSs). Throughput subnets and s-transitions are presented. Two FMS examples containing nonexponential distributions which were analyzed in previous papers by queuing theory and probability theory, respectively, are treated using GSPNs developed using throughput subnets and s-transitions. The GSPN results agree with the previous results, and developing and analyzing the GSPN models are straightforward and relatively easy compared to other methodologies.

Watson, James F., III↗

NASA NTRS1996

Evaluation of Scheduling Methods for Multiple Runways

Several scheduling strategies are analyzed in order to determine the most efficient means of scheduling aircraft when multiple runways are operational and the airport is operating at different utilization rates. The study compares simulation data for two and three runway scenarios to results from queuing theory for an M/D/n queue. The direction taken, however, is not to do a steady-state, or equilibrium, analysis since this is not the case during a rush period at a typical airport. Instead, a transient analysis of the delay per aircraft is performed. It is shown that the scheduling strategy that reduces the delay depends upon the density of the arrival traffic. For light traffic, scheduling aircraft to their preferred runways is sufficient; however, as the arrival rate increases, it becomes more important to separate traffic by weight class. Significant delay reduction is realized when aircraft that belong to the heavy and small weight classes are sent to separate runways with large aircraft put into the 'best' landing slot.

Bolender, Michael A.↗

NASA NTRS1996

Evolving Requirements for Magnetic Tape Data Storage Systems

Magnetic tape data storage systems have evolved in an environment where the major applications have been back-up/restore, disaster recovery, and long term archive. Coincident with the rapidly improving price-performance of disk storage systems, the prime requirements for tape storage systems have remained: (1) low cost per MB, (2) a data rate balanced to the remaining system components. Little emphasis was given to configuring the technology components to optimize retrieval of the stored data. Emerging new applications such as network attached high speed memory (HSM), and digital libraries, place additional emphasis and requirements on the retrieval of the stored data. It is therefore desirable to consider the system to be defined both by STorage And Retrieval System (STARS) requirements. It is possible to provide comparative performance analysis of different STARS by incorporating parameters related to (1) device characteristics, and (2) application characteristics in combination with queuing theory analysis. Results of these analyses are presented here in the form of response time as a function of system configuration for two different types of devices and for a variety of applications.

Gniewek, John J.↗

NASA NTRSDate not supplied

Introducing Tropical Geometric Approaches to Delay Tolerant Networking Optimization

Delay Tolerant Networking (DTN) is the standard approach to the networking of space systems with the goal of supporting the Solar System Internet (SSI). Current space networks have a small scale and often depend on rigorously scheduled (pre-determined) contact opportunities; this manual approach inhibits scalability. The goal of this paper is to recast these scheduling problems in order to apply the optimization machinery of tropical geometry. Contact opportunities in space are dependent on such factors as orbital mechanics and asset availability, which induce time-varying connectivity; indeed, end-to-end connectivity might never occur. Routing optimization within this structure is classically difficult and typically utilizes Dijkstra's algorithm as applied to contact graphs. Alternatively, we follow the successes of tropical geometry in train schedule optimization, job assignments, and even traditional networking, by extending this approach to this more general (i.e. disconnected) problem space. These successes imply tropical geometry provides a useful framework in the context of DTNs, starting with applications to queuing theory and long-haul links. Recently, tropical geometry has been applied to parametric path optimization on graphs with variable edge weights. In this work, we extend these advances to account for the problem of routing in a space network, and find that tropical geometry is well-suited to the challenges offered by this new setting, including contact schedules featuring probabilities. Our approach leverages the combinatorial nature of the problem to give feasible shortest path trees in the presence of variable channel conditions and latency, evolving topologies, and uncertainty inherent in space routing. We discuss our tropical approach to DTN for two Python implementations, a Verilog Tropical ALU implementation, tropical frameworks for other parametric graph problems, and solution stability. Lastly, a program for future work is included to illuminate the path ahead.

Delay Tolerant Networking↗

NASA NTRS1995

Design of object-oriented distributed simulation classes

Distributed simulation of aircraft engines as part of a computer aided design package is being developed by NASA Lewis Research Center for the aircraft industry. The project is called NPSS, an acronym for 'Numerical Propulsion Simulation System'. NPSS is a flexible object-oriented simulation of aircraft engines requiring high computing speed. It is desirable to run the simulation on a distributed computer system with multiple processors executing portions of the simulation in parallel. The purpose of this research was to investigate object-oriented structures such that individual objects could be distributed. The set of classes used in the simulation must be designed to facilitate parallel computation. Since the portions of the simulation carried out in parallel are not independent of one another, there is the need for communication among the parallel executing processors which in turn implies need for their synchronization. Communication and synchronization can lead to decreased throughput as parallel processors wait for data or synchronization signals from other processors. As a result of this research, the following have been accomplished. The design and implementation of a set of simulation classes which result in a distributed simulation control program have been completed. The design is based upon MIT 'Actor' model of a concurrent object and uses 'connectors' to structure dynamic connections between simulation components. Connectors may be dynamically created according to the distribution of objects among machines at execution time without any programming changes. Measurements of the basic performance have been carried out with the result that communication overhead of the distributed design is swamped by the computation time of modules unless modules have very short execution times per iteration or time step. An analytical performance model based upon queuing network theory has been designed and implemented. Its application to realistic configurations has not been carried out.

Schoeffler, James D.↗

NASA NTRS1995

Design of Object-Oriented Distributed Simulation Classes

Distributed simulation of aircraft engines as part of a computer aided design package being developed by NASA Lewis Research Center for the aircraft industry. The project is called NPSS, an acronym for "Numerical Propulsion Simulation System". NPSS is a flexible object-oriented simulation of aircraft engines requiring high computing speed. It is desirable to run the simulation on a distributed computer system with multiple processors executing portions of the simulation in parallel. The purpose of this research was to investigate object-oriented structures such that individual objects could be distributed. The set of classes used in the simulation must be designed to facilitate parallel computation. Since the portions of the simulation carried out in parallel are not independent of one another, there is the need for communication among the parallel executing processors which in turn implies need for their synchronization. Communication and synchronization can lead to decreased throughput as parallel processors wait for data or synchronization signals from other processors. As a result of this research, the following have been accomplished. The design and implementation of a set of simulation classes which result in a distributed simulation control program have been completed. The design is based upon MIT "Actor" model of a concurrent object and uses "connectors" to structure dynamic connections between simulation components. Connectors may be dynamically created according to the distribution of objects among machines at execution time without any programming changes. Measurements of the basic performance have been carried out with the result that communication overhead of the distributed design is swamped by the computation time of modules unless modules have very short execution times per iteration or time step. An analytical performance model based upon queuing network theory has been designed and implemented. Its application to realistic configurations has not been carried out.

Schoeffler, James D.↗

NASA NTRS1975

Cost performance satellite design using queueing theory

A modified Poisson arrival, infinite server queuing model is used to determine the effects of limiting the number of broadcast channels (C) of a direct broadcast satellite used for public service purposes (remote health care, education, etc.). The model is based on the reproductive property of the Poisson distribution. A difference equation has been developed to describe the change in the Poisson parameter. When all initially delayed arrivals reenter the system a (C plus 1) order polynomial must be solved to determine the effective value of the Poisson parameter. When less than 100% of the arrivals reenter the system the effective value must be determined by solving a transcendental equation. The model was used to determine the minimum number of channels required for a disaster warning satellite without degradation in performance. Results predicted by the queuing model were compared with the results of digital simulation.

Hein, G. F.↗

DOE OSTI2023

Kullback–Leibler Divergence of an Open-Queuing Network of a Cell-Signal-Transduction Cascade

Queuing networks (QNs) are essential models in operations research, with applications in cloud computing and healthcare systems. However, few studies have analyzed the cell’s biological signal transduction using QN theory. This study entailed the modeling of signal transduction as an open Jackson’s QN (JQN) to theoretically determine cell signal transduction, under the assumption that the signal mediator queues in the cytoplasm, and the mediator is exchanged from one signaling molecule to another through interactions between the signaling molecules. Each signaling molecule was regarded as a network node in the JQN. The JQN Kullback–Leibler divergence (KLD) was defined using the ratio of the queuing time (λ) to the exchange time (μ), λ/μ. The mitogen-activated protein kinase (MAPK) signal-cascade model was applied, and the KLD rate per signal-transduction-period was shown to be conserved when the KLD was maximized. Our experimental study on MAPK cascade supported this conclusion. This result is similar to the entropy-rate conservation of chemical kinetics and entropy coding reported in our previous studies. Thus, JQN can be used as a novel framework to analyze signal transduction.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Sheaf Theoretic Models for Routing in Delay Tolerant Networks

One key to communications scalability is routing; as such the goal of this paper is to build upon successful efforts towards general routing for space-based networks. With the ever-increasing accessibility of space, the number of assets is increasing, which becomes a critical communications burden in terms of scheduling, spectrum allocation, and resource allocation. In order to mitigate these concerns, a true networking approach is necessary; a standard approach for space systems is Delay Tolerant Networking (DTN). For DTN to be a meaningful answer to the Solar System Internet (SSI) question, DTN must offer meaningful routing solutions that span the heterogeneous collection of links and nodes. This, in turn, depends on the general structure of these disconnected networks -- a structure that remains largely unknown. In ground communications networks, routing decisions are made based on several pathfinding algorithms working in tandem. In previous work, we modeled Dijkstra's pathfinding algorithm using sheaves and provided a more general framework for determining paths using sheaves over graphs. Continuing our sheaf-theoretic approach, we introduce here an expansion of our pathfinding sheaf to handle more general information, and we expand on additional pathfinding algorithms that can be represented using sheaves. Moreover, we demonstrate means of combining multiple algorithms into a single sheaf structure so that changes of scale can be presented in the language of sheaves. In addition, space communications networks rely upon radio transmitter antennas which can establish broadcast and multicast communications options, rather than the primarily unicast options available to wired networks. Last year, we also introduced a multicast routing sheaf for presenting broadcast, unicast, and multicast communications over a graph. Extending that work, we also introduce queuing sheaves so that we can blend these communications options together to simulate a variety of routing options across space networks. In addition, we include examples to illustrate the applicability of this abstract theory to routing in disconnected networks.

Robert Short↗