Equilibrium Point Analysis Research Articles

A comparison of construction methods for mac and llc protocols in satellite packet communication networks

AbstractThis paper discusses the layered construction of the OSI second layer (data link layer) in the satellite packet communication network from the viewpoint of the system performance. The isolated‐type system, where the media access control (MAC) sublayer and logical link control (LLC) sublayer are defined independently, and the combined‐type system, where they are defined in a related way, are considered. The performances of those two systems are compared, using the throughput and the average response time as the evaluation criteria.The TDMA‐Reservation and the slotted‐ALOHA are considered as the MAC protocol. The connection‐oriented type is considered as the LLC protocol. As to the TDMA‐Reservation communication network, the isolated‐type system is analyzed by the equilibrium point analysis. Then the performances of the isolated type and the combined type are compared by the analysis and simulation.It is shown quantitatively by comparison that the performance of the isolated type is always better than that of the combined type. As to the slotted‐ALOHA communication network, it is shown by simulation that little difference is observed in the performances of the isolated and the combined types.

Performance analysis of slotted aloha over time‐varying channels

AbstractThis paper considers a slotted ALOHA network which consists of a central base station and many mobile terminals. In classical performance analyses of random access networks, a channel between the station and a terminal is assumed to be always in a good state. However, this is not the case in mobile radio networks since the channel suffers from many factors such as fading, shadowing, and so on. Moreover, the channel condition changes with the terminal location.In this paper, a simple channel model is used to consider the effects of time‐varying channels in a random access network. The channel model assumed in this paper has three states: shadowing, good, and bad. The transitions between the channel states are described by a Markov chain. The dynamic performance of a slotted ALOHA network over such time‐varying channels is evaluated by means of the equilibrium point analysis. Then the influence of the time‐varying channel on the throughput performance of a slotted ALOHA network is studied.

Performance approximation of a multi-base station slotted ALOHA for wireless LAN's

It has been reported that the capture effect can improve the performance of slotted ALOHA systems. Further improvement can be expected when the number of base stations is increased. The performance of such slotted ALOHA systems with multiple base stations is analyzed with the aid of the equilibrium point analysis. Not only the capture effect but also the packet dropping due to the finite number of retransmission trials are taken into account. The numerical results indicate that the finite number of retransmission trials mainly contributes to the improvement of the packet dropping probability in the range of the light input traffic, while the number of base stations mainly contributes to the improvement of the overall throughput and the average transmission delay in the range of the heavy input traffic. >

Equivalence of approximation techniques for solution of multidimensional Markov chains in network modelling

In principle, the access protocols of many communication or computer networks can be modelled as discrete-time Markov chains. In practice, these Markov chains are multidimensional, and due to the vast state space are unsolvable without the use of approximation techniques. Two such techniques are equilibrium point analysis and single station superposition. It is shown that these two seemingly disparate methods are actually equivalent under certain constraints.

Performance of PRMA: a packet voice protocol for cellular systems

Equilibrium point analysis is used to evaluate system behavior in a packet reservation multiple access (PRMA) protocol based network. The authors derive the probability of packet dropping given the number of simultaneous conversations. The authors establish conditions for system stability and efficiency. Numerical calculations based on the theory show close agreement with computer simulations. They also provide valuable guides to system design. Because PRMA is a statistical multiplexer, the channel becomes congested when too many terminals are active. For a particular example it is shown that speech activity detection permits 37 speech terminals to share a PRMA channel with 20 slots per frame, with a packet dropping probability of less than 1%.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A performance comparison of link level connection schemes in csma/cd networks

AbstractThis paper considers the logical link control (LLC) sublayer in the CSMA/CD local area network, and compares analytically the performance of connection‐oriented (CO) and connectionless (CL) protocols. As the medium access protocol, slotted nonpersistent CSMA/CD with a priority assigned to some types of frames is employed. In comparison, the overhead for connection establishment/release in the CO‐LLC protocol, and the receiver‐buffer overflow in the CL‐LLC protocol are especially considered, and the two kinds of protocols are compared.In the CO‐LLC protocol, a connection is established corresponding to a message. Employing the technique of equilibrium point analysis, the throughput and the average response time of the two kinds of LLC protocols are derived. To compare the performance of the two kinds of protocols, the receiver‐buffer size is kept constant, and the average number of data frames in a message is varied. As a result, it is shown that the CL‐LLC protocol is better than the CO‐LLC protocol when the average number of data frames is sufficiently less than the receiver‐buffer size, but the order is reversed when the average number of data frames is increased.

Equilibrium point analysis of memory interference in multiprocessor systems

An approximate analytic tool called equilibrium point analysis is applied to the problem of memory interference in multiprocessor systems. It is a simple and powerful analytic tool based on the fluid approximation and has been widely used for packet broadcast systems. It is shown that quite general multiprocessor systems can be studied quite simply with this technique, these systems include those made up of many classes of processors and memory modules with arbitrary static memory reference patterns, and systems with bus connections between processors and memories. In most cases, the approximation is shown to be sufficiently good. One of the advantages of this technique is that the error is smaller for larger systems for which no appropriate analytic tools have existed until now.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance analysis of a buffered CSMA/CD system

AbstractMost of the performance analyses of CSMA/CD systems have assumed that each user has a buffer space for only one packet. Using the technique of equilibrium point analysis, this paper analyzes the dynamic behavior of a slotted nonpersistent CSMA/CD system with a finite number of users, each of whom has a finite buffer space for more than one packet. Two schemes of packet transmission are studied: (1) once a user captures the channel, he continuously transmits all of the packets which have been stored in his buffer by the instant of the capture (gating type); and (2)he transmits at most one packet at a time (limiting type). First the gating type is analyzed, and its throughput, its average packet delay and its system stability are evaluated. An approximate probability distribution for the number of packets in the buffer space of a user is derived. On the basis of these analytic results, we study how to select both the buffer size and the rescheduling probability of packets which guarantee the system stability, keep the probability of buffer overflow sufficiently small and at the same time minimize the average packet delay. The two schemes are compared and it is shown that the gating scheme out performs the limiting scheme in terms of average packet delay and the average and variance for the number of packets in a buffer.

The SRUC Protocol for Satellite Packet Communication--A Performance Analysis

SRUC is an adaptive multiple access protocol which combines the slotted ALOHA protocol and a reservation protocol; it switches from one to the other according to the state of the channel. This paper studies SRUC with a go-back- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> ARQ scheme (SRUC/GBN) in a satellite communication environment to improve the performance over SRUC with a stop-and-wait ARQ scheme (SRUC/SAW) previously studied. The performance of SRUC/GBN is analyzed in this paper, it is assumed that each user handles one message at a time and that the number of packets in a message is geometrically distributed. An approximate Markovian model for SRUC/GBN is developed which has a multidimensional state vector. The model is analyzed by the technique of equilibrium point analysis. The throughput and average message delay performance is derived. Numerical results from both analysis and simulation are given. The performance of SRUC/GBN is also compared with that of SRUC/SAW and other multiple access protocols.

Dynamic Behavior of a CSMA-CD System with a Finite Population of Buffered Users

In packet broadcast networks with buffered users, queues of packets at the users interfere with each other through a shared broadcast channel. Therefore, it is difficult to analyze the performance of such Systems by classical queueing theory. This paper provides an approximate performance analysis of a slotted nonpersistent CSMA-CD system with a finite number of users, each having a buffer of finite capacity. We develop an approximate Markovian model of the system with a multidimensional state vector. To analyze the model, We utilize an approximate analytical technique called equilibrium point analysis (EPA). Then, the throughput and average packet delay characteristics are obtained and the system stability behavior is demonstrated. An approximate expression is also derived for the probability distribution of the number of packets in a buffer. Numerical results from both analysis and simulation are given to illustrate the accuracy of those analytic results. Using the analytic results, we examine the effect of the collision detection capability on the system performance. Furthermore, we consider how to select both the rescheduling probability and the buffer size that guarantee the system stability, keep the probability of buffer overflow sufficiently small, and at the same time minimize the average packet delay.

Equilibrium point analysis of memory interference in multiprocessor systems

AbstractAn approximate analytic tool called equilibrium point analysis is applied to the problem of memory interference in multiprocessor systems. This is a simple and powerful analytic tool based on the fluid approximation. It has been used widely in packet broadcast systems. It is shown that quite general multiprocessor systems can be studied by this technique with amazing simplicity. For example, systems made up of many classes of processors and memory modules with arbitrary static memory reference patterns and systems with dynamic memory reference patterns are considered. In most cases, the approximation of the analysis is shown to be sufficiently good. One of the advantages of this technique is that the error is smaller for larger systems for which there have been no appropriate analytic tools thus far.

A Reservation Protocol for Satellite Packet Communication--A Performance Analysis and Stability Considerations

The dynamic behavior of a reservation system with a slotted ALOHA reservation channel is analyzed in this paper. It is assumed that each user handles one message at a time and that each message consists of a group of packets with a general probability distribution for group size. An approximate Markovian model of the system is developed on the assumption that the state transition can occur only at the beginning of each frame. The model is analyzed by an approximate analytical technique called equilibrium point analysis. The throughput and average message delay characteristics are obtained, and the system stability behavior is demonstrated. A procedure is also given to get the optimum set of system parameters under constraint that the system is stable.

Multiple-access protocols for satellite packet communication networks: A performance comparison

This paper considers satellite packet communication networks with a large population of bursty users and presents an analytic comparison of the throughput versus average message delay trade-off characteristics of multiple-access protocols. The following six multiple-access protocols are examined: 1) slotted ALOHA, 2) reservation-ALOHA, 3) a reservation protocol with a slotted ALOHA reservation channel, 4) a reservation protocol with a TDMA reservation channel, 5) SRUC (Split Reservation Upon Collision), and 6) fixed assigned TDMA. All the protocols are required to ensure that all packets of a message are correctly received in the proper order at the destination. Then, a unified presentation of the delay-throughput performance of the protocols is given by means of an analytical technique called equilibrium point analysis. The throughput versus average message delay tradeoff characteristics are compared taking into account the system stability.

Stability and Performance of the R-Aloha Packet Broadcast System

The dynamic behavior of the R-ALOHA packet broadcast system with multipacket messages is analyzed in this paper. It is assumed that each user handles one message at a time and the number of packets in a message is geometrically distributed. A Markovian model of the system is first formulated which explicitly contains the influence of the propagation delay of the broadcast channel. An approximate technique called equilibrium point analysis (EPA) is utilized to analyze the multidimensional Markov chain. The system stability behavior and the throughput-average message delay performance are demonstrated by the EPA. Numerical results from both analysis and simulation are given to assess the accuracy of the analytic results. Applying the analytic results to the slotted ALOHA with single packet messages, we prove mathematically that a method by Kleinrock and Lam for taking into account the influence of the propagation delay is an excellent approximation.

Stability considerations and dynamic control in csma packet radio networks

AbstractSo far, many proposals have been put forward for increasing the channel capacity of the ALOHA system. Among these is the use of the CSMA system which is known to improve to a great extent the properties of the random access system by ground radio or cable. So far, the slotted CSMA system has been studied in detail for its dynamic characteristics and traffic control effect. But in the case of non‐slotted CSMA, except that its capacity is almost the same, a detailed analysis has yet to be done. In this paper, the dynamic characteristics of the non‐slotted CSMA due to ground radio has been investigated by equilibrium point analysis. It is revealed that the throughput characteristics of the non‐slotted CSMA system are almost similar to those for the slotted CSMA system, but the system stability is quite poor. Next it is proposed that a simple traffic control be applied in the non‐slotted CSMA and the improvement in stability has been studied. It is shown that the dispersion of the packet delay is increased slightly but the operation due to this simple control system can be made sufficiently stable. Thus it is shown that it is not necessary to apply the complex terminal control, i.e., synchronizing the transmission with the slot, for the system stability.

Effect of cortisone in experimental syphilis in rabbits.

<h3>Abstract</h3> In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.