Most of the internet users connect through wireless networks. Majorpart of internet traffic is carried by Transmission Control Protocol (TCP). It hassome design constraints while operated across wireless networks. TCP...Most of the internet users connect through wireless networks. Majorpart of internet traffic is carried by Transmission Control Protocol (TCP). It hassome design constraints while operated across wireless networks. TCP is the traditional predominant protocol designed for wired networks. To control congestionin the network, TCP used acknowledgment to delivery of packets by the end host.In wired network, packet loss signals congestion in the network. But rather inwireless networks, loss is mainly because of the wireless characteristics such asfading, signal strength etc. When a packet travels across wired and wireless networks, TCP congestion control theory faces problem during handshake betweenthem. This paper focuses on finding this misinterpretation of the losses using crosslayer approach. This paper focuses on increasing bandwidth usage by improvingTCP throughput in wireless environments using cross layer approach and hencenamed the proposed system as CRLTCP. TCP misinterprets wireless loss as congestion loss and unnecessarily reduces congestion window size. Using the signalstrength and frame error rate, the type of loss is identified and accordingly theresponse of TCP is modified. The results show that there is a significant improvement in the throughput of proposed TCP upon which bandwidth usage isincreased.展开更多
With the emerging diverse applications in data centers,the demands on quality of service in data centers also become diverse,such as high throughput of elephant flows and low latency of deadline-sensitive flows.Howeve...With the emerging diverse applications in data centers,the demands on quality of service in data centers also become diverse,such as high throughput of elephant flows and low latency of deadline-sensitive flows.However,traditional TCPs are ill-suited to such situations and always result in the inefficiency(e.g.missing the flow deadline,inevitable throughput collapse)of data transfers.This further degrades the user-perceived quality of service(QoS)in data centers.To reduce the flow completion time of mice and deadline-sensitive flows along with promoting the throughput of elephant flows,an efficient and deadline-aware priority-driven congestion control(PCC)protocol,which grants mice and deadline-sensitive flows the highest priority,is proposed in this paper.Specifically,PCC computes the priority of different flows according to the size of transmitted data,the remaining data volume,and the flows’deadline.Then PCC adjusts the congestion window according to the flow priority and the degree of network congestion.Furthermore,switches in data centers control the input/output of packets based on the flow priority and the queue length.Different from existing TCPs,to speed up the data transfers of mice and deadline-sensitive flows,PCC provides an effective method to compute and encode the flow priority explicitly.According to the flow priority,switches can manage packets efficiently and ensure the data transfers of high priority flows through a weighted priority scheduling with minor modification.The experimental results prove that PCC can improve the data transfer performance of mice and deadline-sensitive flows while guaranting the throughput of elephant flows.展开更多
The goal of this paper is to propose a fast and secure multi-stage image compression-decompression system by using a wireless network between two Personal Computers (PCs). In this paper, the Principal Component Analys...The goal of this paper is to propose a fast and secure multi-stage image compression-decompression system by using a wireless network between two Personal Computers (PCs). In this paper, the Principal Component Analysis (PCA) technique is used for multi-stage image compression and Inverse Principal Component Analysis (IPCA) for multi-stage image decompression. The first step of the proposed system is to select the input image, the second step is to perform PCA up to 9 times on the input image, this compression, and after multi-stage compression process then the third step begins by transforming across wireless Ad hoc Network (WANET) to the second computing device, forth step start with multi-stage decompression process up 9 times. The proposed system for different images is transferred over the wireless network using Transmission Control Protocol/Internet Protocol (TCP/IP), which is programmed using the network role property of the MATLAB program. The proposed system implements 25 different images correctly (100%). The main contribution of this paper is that we are dealing with the black image at the end of the compressed process ad start with a black image at the start of the decompressed process of this proposed system. In this work, the compressed and uncompressed images are compared with each other in their size and transmission time. This system can be very useful in networks because they provide a high level of protection to the transmitted data from hackers because they cannot guess how much the image has been compressed or what kind of information the image represents.展开更多
Vehicle Ad hoc Networks(VANETs)have high mobility and a rando-mized connection structure,resulting in extremely dynamic behavior.Several challenges,such as frequent connection failures,sustainability,multi-hop data tr...Vehicle Ad hoc Networks(VANETs)have high mobility and a rando-mized connection structure,resulting in extremely dynamic behavior.Several challenges,such as frequent connection failures,sustainability,multi-hop data transfer,and data loss,affect the effectiveness of Transmission Control Protocols(TCP)on such wireless ad hoc networks.To avoid the problem,in this paper,mobility-aware zone-based routing in VANET is proposed.To achieve this con-cept,in this paper hybrid optimization algorithm is presented.The hybrid algo-rithm is a combination of Ant colony optimization(ACO)and artificial bee colony optimization(ABC).The proposed hybrid algorithm is designed for the routing process which is transmitting the information from one place to another.The optimal routing process is used to avoid traffic and link failure.Thefitness function is designed based on Link stability and Residual energy.The validation of the proposed algorithm takes solution encoding,fitness calculation,and updat-ing functions.To perform simulation experiments,NS2 simulator software is used.The performance of the proposed approach is analyzed based on different metrics namely,delivery ratio,delay time,throughput,and overhead.The effec-tiveness of the proposed method compared with different algorithms.Compared to other existing VANET algorithms,the hybrid algorithm has proven to be very efficient in terms of packet delivery ratio and delay.展开更多
In this paper, we propose a new mechanism called explicit rate notification(ERN) to be used in end-to-end communications. The ERN scheme encodes in the header of transmission control protocol(TCP) packets information ...In this paper, we propose a new mechanism called explicit rate notification(ERN) to be used in end-to-end communications. The ERN scheme encodes in the header of transmission control protocol(TCP) packets information about the sending rate and the round trip time(RTT) of the flows. This new available information to the intermediate nodes(routers) is used to improve fairness, increase utilization, decrease the number of drops, and minimize queueing delays. Thus, it induces a better management of the queue. A comparison of our scheme with preexistent schemes, like the explicit congestion notification scheme, shows the effectiveness of the proposed mechanism.展开更多
A novel and efficient method to evaluate the transmission control protocol (TCP) performance over satellite links is presented. A TCP module is divided into three functional blocks, namely data processing, congestio...A novel and efficient method to evaluate the transmission control protocol (TCP) performance over satellite links is presented. A TCP module is divided into three functional blocks, namely data processing, congestion control and error control The re-established TCP module is easy to update TCP congestion control strategy or error control strategy. With the proposed analysis approach, the interactions between different congestion control and error control mechanisms, as well as the performanee of various combination protocols in satellite environments have been investigated. Simulation results obtained through a series of experiments have shown that SNACK-based error control strategy can perform well with any other congestion control strategy. The best performanee can be achieved by TCP NewReno congestion control strategy and SNACK-based error control strategy.展开更多
Αcloud-based home electricity data-monitoring system,which is based on an Arduino Mega controller,is proposed for monitoring the electricity consumption(electrical power)and power quality(PQ)in home.This system is al...Αcloud-based home electricity data-monitoring system,which is based on an Arduino Mega controller,is proposed for monitoring the electricity consumption(electrical power)and power quality(PQ)in home.This system is also capable of monitoring the fundamental frequency and supply-voltage transients to ensure that the appliances operate in a safe operation range.The measured data(voltage and current)are transmitted through a Wi Fi device between the Arduino controller and server.The transmission control protocol(TCP)server is set up to acquire the high-data transmission rate.The server system immediately displays the calculated parameters and the waveform of the acquired signal.A comparison with a standard measurement device shows that the proposed system,which can be built at a low cost,exhibits the same functions as a factory product.展开更多
In data centers, the transmission control protocol(TCP) incast causes catastrophic goodput degradation to applications with a many-to-one traffic pattern. In this paper, we intend to tame incast at the receiver-side a...In data centers, the transmission control protocol(TCP) incast causes catastrophic goodput degradation to applications with a many-to-one traffic pattern. In this paper, we intend to tame incast at the receiver-side application. Towards this goal, we first develop an analytical model that formulates the incast probability as a function of connection variables and network environment settings. We combine the model with the optimization theory and derive some insights into minimizing the incast probability through tuning connection variables related to applications. Then,enlightened by the analytical results, we propose an adaptive application-layer solution to the TCP incast.The solution equally allocates advertised windows to concurrent connections, and dynamically adapts the number of concurrent connections to the varying conditions. Simulation results show that our solution consistently eludes incast and achieves high goodput in various scenarios including the ones with multiple bottleneck links and background TCP traffic.展开更多
This paper presents a novel way to improve Transmission Control Protocol (TCP) performance of the users at the edge areas of the macro cells in Long Term Evolution Advanced (LTE-A) systems. Previous works on improving...This paper presents a novel way to improve Transmission Control Protocol (TCP) performance of the users at the edge areas of the macro cells in Long Term Evolution Advanced (LTE-A) systems. Previous works on improving wireless TCP performance are reviewed and current considerations on TCP in LTE-A are explained. However, those solutions are neither too complex nor limited to some presuppositions which are too restricting for the deployment of LTE-A networks. In this paper a substituted TCP acknowledgement transmission scheme based on Automatic Repeat reQuest (ARQ) information in layer 2 is proposed. The simulation result shows that the proposed method can reduce the delay and improve the throughput of the edging users of the cell, as well as reducing radio resources in LTE-A macro cells.展开更多
Concurrent multipath transfer(CMT) using stream control transmission protocol(SCTP) multihoming has become an appealing option to increase the throughput and improve the performance of increasingly bandwidth-hungr...Concurrent multipath transfer(CMT) using stream control transmission protocol(SCTP) multihoming has become an appealing option to increase the throughput and improve the performance of increasingly bandwidth-hungry applications.To investigate the rate allocation for applications in CMT,this paper analyzes the capacities of paths shared by competing sources,then proposes the rate allocation model for elastic flows based on the framework of network utility maximization(NUM).In order to obtain the global optimum of the model,a distributed algorithm is presented which depends only on local available information.Simulation results confirm that the proposed algorithm can achieve the global optimum within reasonable convergence times.展开更多
A novel assembly control algorithm named burst-size feedback adaptive assembly period (BFAAP) is proposed. The major difference between BFAAP and other similar adaptive assembly algorithms is that the control curve ...A novel assembly control algorithm named burst-size feedback adaptive assembly period (BFAAP) is proposed. The major difference between BFAAP and other similar adaptive assembly algorithms is that the control curve of BFAAP is dynamically adjusted according to the feedback of outgoing burst size. BFAAP is compared with two typical algorithms fixed assembly period (FAP) and min-burst length max- assembly period (MBMAP) in simulation in terms of burst size distribution and assembly period. Moreover, the transmission control protocol (TCP) performance over BFAAP is also considered and simulated.展开更多
There is a lack of appropriate guidelines for realistic user traces, mobility models, routing protocols, considerations of real-life challenges, etc. for general-purpose mobile ad hoc networks (MANET). In this paper...There is a lack of appropriate guidelines for realistic user traces, mobility models, routing protocols, considerations of real-life challenges, etc. for general-purpose mobile ad hoc networks (MANET). In this paper, four laptops are used in an open field environment in four scenarios to evaluate the performances of Internet control message protocol (ICMP) based ping and transmission control protocol (TCP) based streaming video applications using optimised link state routing (OLSR) implementation in an IEEE 802.11g wireless network. Corresponding simulations are developed in Network Simulator ns-2 by setting simulation parameters according to the real experiments. Difficulties faced to regenerate real-life scenarios have been discussed and the gaps between reality and simulation are identified. A setup guideline to produce realistic simulation results has been established.展开更多
Designing a robust active queue management(RAQM)is mandatory to avoid congestion in networks with wireless access links,because transmission control protocol(TCP)can detect con-gestion after its occurrence in a commun...Designing a robust active queue management(RAQM)is mandatory to avoid congestion in networks with wireless access links,because transmission control protocol(TCP)can detect con-gestion after its occurrence in a communication network and wireless links suffer from bottleneck capacity variations caused by fading and packet error rate(PER)in the acknowledgement pack-ets.Furthermore,the average window size cannot be measured explicitly from the output signal and input and state delay are imposed to a network,which complicate theRAQMdesign problem in nonlinear models.So,the main contribution of this study is to design a robust observer based control procedure based on integral sliding mode protocol to estimate the average window size,to control congestion in a TCP/RAQM network and to compensate input and state delay.Sim-ulation results via professional simulator NS-2 and SIMULINK confirm that the procedure can effectively estimate the window size and can robustly avoid congestion.展开更多
Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is...Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.展开更多
文摘Most of the internet users connect through wireless networks. Majorpart of internet traffic is carried by Transmission Control Protocol (TCP). It hassome design constraints while operated across wireless networks. TCP is the traditional predominant protocol designed for wired networks. To control congestionin the network, TCP used acknowledgment to delivery of packets by the end host.In wired network, packet loss signals congestion in the network. But rather inwireless networks, loss is mainly because of the wireless characteristics such asfading, signal strength etc. When a packet travels across wired and wireless networks, TCP congestion control theory faces problem during handshake betweenthem. This paper focuses on finding this misinterpretation of the losses using crosslayer approach. This paper focuses on increasing bandwidth usage by improvingTCP throughput in wireless environments using cross layer approach and hencenamed the proposed system as CRLTCP. TCP misinterprets wireless loss as congestion loss and unnecessarily reduces congestion window size. Using the signalstrength and frame error rate, the type of loss is identified and accordingly theresponse of TCP is modified. The results show that there is a significant improvement in the throughput of proposed TCP upon which bandwidth usage isincreased.
基金supported part by the National Natural Science Foundation of China(61601252,61801254)Public Technology Projects of Zhejiang Province(LG-G18F020007)+1 种基金Zhejiang Provincial Natural Science Foundation of China(LY20F020008,LY18F020011,LY20F010004)K.C.Wong Magna Fund in Ningbo University。
文摘With the emerging diverse applications in data centers,the demands on quality of service in data centers also become diverse,such as high throughput of elephant flows and low latency of deadline-sensitive flows.However,traditional TCPs are ill-suited to such situations and always result in the inefficiency(e.g.missing the flow deadline,inevitable throughput collapse)of data transfers.This further degrades the user-perceived quality of service(QoS)in data centers.To reduce the flow completion time of mice and deadline-sensitive flows along with promoting the throughput of elephant flows,an efficient and deadline-aware priority-driven congestion control(PCC)protocol,which grants mice and deadline-sensitive flows the highest priority,is proposed in this paper.Specifically,PCC computes the priority of different flows according to the size of transmitted data,the remaining data volume,and the flows’deadline.Then PCC adjusts the congestion window according to the flow priority and the degree of network congestion.Furthermore,switches in data centers control the input/output of packets based on the flow priority and the queue length.Different from existing TCPs,to speed up the data transfers of mice and deadline-sensitive flows,PCC provides an effective method to compute and encode the flow priority explicitly.According to the flow priority,switches can manage packets efficiently and ensure the data transfers of high priority flows through a weighted priority scheduling with minor modification.The experimental results prove that PCC can improve the data transfer performance of mice and deadline-sensitive flows while guaranting the throughput of elephant flows.
文摘The goal of this paper is to propose a fast and secure multi-stage image compression-decompression system by using a wireless network between two Personal Computers (PCs). In this paper, the Principal Component Analysis (PCA) technique is used for multi-stage image compression and Inverse Principal Component Analysis (IPCA) for multi-stage image decompression. The first step of the proposed system is to select the input image, the second step is to perform PCA up to 9 times on the input image, this compression, and after multi-stage compression process then the third step begins by transforming across wireless Ad hoc Network (WANET) to the second computing device, forth step start with multi-stage decompression process up 9 times. The proposed system for different images is transferred over the wireless network using Transmission Control Protocol/Internet Protocol (TCP/IP), which is programmed using the network role property of the MATLAB program. The proposed system implements 25 different images correctly (100%). The main contribution of this paper is that we are dealing with the black image at the end of the compressed process ad start with a black image at the start of the decompressed process of this proposed system. In this work, the compressed and uncompressed images are compared with each other in their size and transmission time. This system can be very useful in networks because they provide a high level of protection to the transmitted data from hackers because they cannot guess how much the image has been compressed or what kind of information the image represents.
文摘Vehicle Ad hoc Networks(VANETs)have high mobility and a rando-mized connection structure,resulting in extremely dynamic behavior.Several challenges,such as frequent connection failures,sustainability,multi-hop data transfer,and data loss,affect the effectiveness of Transmission Control Protocols(TCP)on such wireless ad hoc networks.To avoid the problem,in this paper,mobility-aware zone-based routing in VANET is proposed.To achieve this con-cept,in this paper hybrid optimization algorithm is presented.The hybrid algo-rithm is a combination of Ant colony optimization(ACO)and artificial bee colony optimization(ABC).The proposed hybrid algorithm is designed for the routing process which is transmitting the information from one place to another.The optimal routing process is used to avoid traffic and link failure.Thefitness function is designed based on Link stability and Residual energy.The validation of the proposed algorithm takes solution encoding,fitness calculation,and updat-ing functions.To perform simulation experiments,NS2 simulator software is used.The performance of the proposed approach is analyzed based on different metrics namely,delivery ratio,delay time,throughput,and overhead.The effec-tiveness of the proposed method compared with different algorithms.Compared to other existing VANET algorithms,the hybrid algorithm has proven to be very efficient in terms of packet delivery ratio and delay.
文摘In this paper, we propose a new mechanism called explicit rate notification(ERN) to be used in end-to-end communications. The ERN scheme encodes in the header of transmission control protocol(TCP) packets information about the sending rate and the round trip time(RTT) of the flows. This new available information to the intermediate nodes(routers) is used to improve fairness, increase utilization, decrease the number of drops, and minimize queueing delays. Thus, it induces a better management of the queue. A comparison of our scheme with preexistent schemes, like the explicit congestion notification scheme, shows the effectiveness of the proposed mechanism.
文摘A novel and efficient method to evaluate the transmission control protocol (TCP) performance over satellite links is presented. A TCP module is divided into three functional blocks, namely data processing, congestion control and error control The re-established TCP module is easy to update TCP congestion control strategy or error control strategy. With the proposed analysis approach, the interactions between different congestion control and error control mechanisms, as well as the performanee of various combination protocols in satellite environments have been investigated. Simulation results obtained through a series of experiments have shown that SNACK-based error control strategy can perform well with any other congestion control strategy. The best performanee can be achieved by TCP NewReno congestion control strategy and SNACK-based error control strategy.
基金supported by MOST under Grant No.106-2221-E-468-011-MY2。
文摘Αcloud-based home electricity data-monitoring system,which is based on an Arduino Mega controller,is proposed for monitoring the electricity consumption(electrical power)and power quality(PQ)in home.This system is also capable of monitoring the fundamental frequency and supply-voltage transients to ensure that the appliances operate in a safe operation range.The measured data(voltage and current)are transmitted through a Wi Fi device between the Arduino controller and server.The transmission control protocol(TCP)server is set up to acquire the high-data transmission rate.The server system immediately displays the calculated parameters and the waveform of the acquired signal.A comparison with a standard measurement device shows that the proposed system,which can be built at a low cost,exhibits the same functions as a factory product.
基金supported by the Fundamental Research Fundsfor the Central Universities under Grant No.ZYGX2015J009the Sichuan Province Scientific and Technological Support Project under Grants No.2014GZ0017 and No.2016GZ0093
文摘In data centers, the transmission control protocol(TCP) incast causes catastrophic goodput degradation to applications with a many-to-one traffic pattern. In this paper, we intend to tame incast at the receiver-side application. Towards this goal, we first develop an analytical model that formulates the incast probability as a function of connection variables and network environment settings. We combine the model with the optimization theory and derive some insights into minimizing the incast probability through tuning connection variables related to applications. Then,enlightened by the analytical results, we propose an adaptive application-layer solution to the TCP incast.The solution equally allocates advertised windows to concurrent connections, and dynamically adapts the number of concurrent connections to the varying conditions. Simulation results show that our solution consistently eludes incast and achieves high goodput in various scenarios including the ones with multiple bottleneck links and background TCP traffic.
基金Partly supported by the Key Project of National Natural Science Foundation of China(No.61231007)863 Hi Tech R&D Program of China(No.2012AA121604)ISTCP(No.2012DFG12010)
文摘This paper presents a novel way to improve Transmission Control Protocol (TCP) performance of the users at the edge areas of the macro cells in Long Term Evolution Advanced (LTE-A) systems. Previous works on improving wireless TCP performance are reviewed and current considerations on TCP in LTE-A are explained. However, those solutions are neither too complex nor limited to some presuppositions which are too restricting for the deployment of LTE-A networks. In this paper a substituted TCP acknowledgement transmission scheme based on Automatic Repeat reQuest (ARQ) information in layer 2 is proposed. The simulation result shows that the proposed method can reduce the delay and improve the throughput of the edging users of the cell, as well as reducing radio resources in LTE-A macro cells.
基金supported by the National Natural Science Foundation of China (60833002)the National Basic Research Program of China (973 Program) (2007CB307100)+2 种基金the National High Technology Research and Development Program of China (863 Program) (2007AA01Z202)the Program for Changjiang Scholars and Innovative Research Team in University (IRT0707)the Program of Introducing Talents of Discipline to Universities (111 Project) (B08002)
文摘Concurrent multipath transfer(CMT) using stream control transmission protocol(SCTP) multihoming has become an appealing option to increase the throughput and improve the performance of increasingly bandwidth-hungry applications.To investigate the rate allocation for applications in CMT,this paper analyzes the capacities of paths shared by competing sources,then proposes the rate allocation model for elastic flows based on the framework of network utility maximization(NUM).In order to obtain the global optimum of the model,a distributed algorithm is presented which depends only on local available information.Simulation results confirm that the proposed algorithm can achieve the global optimum within reasonable convergence times.
基金supported by the New Century 151 Foundation in Zhejiang Province,China
文摘A novel assembly control algorithm named burst-size feedback adaptive assembly period (BFAAP) is proposed. The major difference between BFAAP and other similar adaptive assembly algorithms is that the control curve of BFAAP is dynamically adjusted according to the feedback of outgoing burst size. BFAAP is compared with two typical algorithms fixed assembly period (FAP) and min-burst length max- assembly period (MBMAP) in simulation in terms of burst size distribution and assembly period. Moreover, the transmission control protocol (TCP) performance over BFAAP is also considered and simulated.
文摘There is a lack of appropriate guidelines for realistic user traces, mobility models, routing protocols, considerations of real-life challenges, etc. for general-purpose mobile ad hoc networks (MANET). In this paper, four laptops are used in an open field environment in four scenarios to evaluate the performances of Internet control message protocol (ICMP) based ping and transmission control protocol (TCP) based streaming video applications using optimised link state routing (OLSR) implementation in an IEEE 802.11g wireless network. Corresponding simulations are developed in Network Simulator ns-2 by setting simulation parameters according to the real experiments. Difficulties faced to regenerate real-life scenarios have been discussed and the gaps between reality and simulation are identified. A setup guideline to produce realistic simulation results has been established.
文摘Designing a robust active queue management(RAQM)is mandatory to avoid congestion in networks with wireless access links,because transmission control protocol(TCP)can detect con-gestion after its occurrence in a communication network and wireless links suffer from bottleneck capacity variations caused by fading and packet error rate(PER)in the acknowledgement pack-ets.Furthermore,the average window size cannot be measured explicitly from the output signal and input and state delay are imposed to a network,which complicate theRAQMdesign problem in nonlinear models.So,the main contribution of this study is to design a robust observer based control procedure based on integral sliding mode protocol to estimate the average window size,to control congestion in a TCP/RAQM network and to compensate input and state delay.Sim-ulation results via professional simulator NS-2 and SIMULINK confirm that the procedure can effectively estimate the window size and can robustly avoid congestion.
基金Supported by the National Natural Science Foundation of China(Nos. 60674048,60772053, 60672142,and 60932005)the National Key Basic Research and Development (973) Program of China (Nos.2007CB307100 and 2007CB307105)
文摘Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.