Jaidev Kaniyil

A copy network with shared buffers for large-scale multicast ATM switching

An architecture for the copy network that is an integral part of multicast ATM switches is described. The architecture makes use of the property that the broadcast banyan network (BBN) is nonblocking if the active inputs are cyclically concentrated and the outputs are monotone. In the architecture, by employing a token ring reservation scheme, the outputs of the copy network are reserved before a multicast cell is replicated. By the copy principle, the number of copies requested by a multicast call is not limited by the size of the copy network so that very large multicast switches can be configured in a modular fashion. The sequence of cells is preserved in the structure. Though physically separated, buffers within the copy network are completely shared, so that the throughput can reach 100%, and the cell delay and the cell loss probability can be made to be very small. The cell delay is estimated analytically and by computer simulation, and the results of both are found to agree with each other. The relationship between the cell loss probability under various traffic parameters and buffer sizes is studied by computer simulation. >

A global message network employing low Earth-orbiting satellites

A global message communication network for low-density traffic, using satellites at low altitudes, is described. This network affords around-the-clock service to any part of the globe, including the polar regions. Such a network can accommodate static and mobile user terminals simultaneously. The oblate globe is modeled as a regular polyhedron with 12 facets for setting up the orbits. Satellites are positioned uniformly in low-altitude symmetrical orbits. The symmetrical orbits are those whose axes are symmetrical in the three-dimensional space. The authors study the coverage aspects of the 6-orbit scheme and the 10-orbit scheme, each with satellites deployed at an altitude of 5000 km. At this altitude, the terrestrial user terminals can access satellites at a grazing angle of 45 degrees . The method of access over the crosslinks is the slotted ALOHA scheme. For low-density traffic, the downlink and uplink throughput rates are estimated. Simulation results agree with these analytical estimates for low values of network offered load. >

Performance analysis of a combined random-reservation access scheme

Stability and throughput are investigated for a combined random-reservation access scheme employed in a satellite-based very small aperture terminal (VSAT) packet communication network. The analysis is based on the use of catastrophe theory by which the system behavior is characterized by the cusp catastrophe. A stable region is given in terms of system and user parameters such as packet generation rate, retransmission rate, channel division ratio and propagation delays. A numerical example is given to illustrate the analysis developed. Simulation results agree with the steady-state throughput of the model. >

Heterogeneous ALOHA networks: a sufficient condition for all equilibrium states to be stable

Abstract This paper models and analyzes the stability of a slotted-ALOHA network hosting heterogeneous users. The scheme is modeled by dividing the total user-population into groups of homogeneous users. The behavior of the system is represented by state equations. The stability analysis is carried out by Liapunovs indirect method, in association with the properties of M-matrix, to obtain the sufficient condition for the structural stability of the networks. The analysis also points out the method of hierarchical grouping of the heterogeneous users.

A modular ATM switch for broadband ISDN switching

This paper proposes and analyzes a buffered multistage switch for the ATM switching in the B-ISDN environment. Each stage consists of a switching section and a distributing section, operating in a cut-through switching mode. The implementation of the proposed switch differs from that proposed by Kim and Leon-Garcia [1]. Each switching section is constructed from 1 × 2 switching elements so that, unlike in the scheme of ref. [1], there does not arise collision of packets at the switching section. The distributing section functions both as a concentrator and as a distributor. The proposed switch does not require internal speed up; packet sequence is maintained. The minimum delay of packet in the switch corresponds only to the propagation delay within the switching network. The analysis shows the delay characteristic approaches that achieved in the output buffered switch. The construction of a large switch by the modular addition of the proposed switch is also feasible.

Input buffer limiting: behavior analysis of a node throughout the range of blocking probabilities

A numerical method is suggested for estimating the performance parameters of a node with input buffer limiting, throughout the range of blocking probabilities. Congestion is attributed to the sudden increase in the effective service time when the input rate increases. This sudden increase, resulting in the thrashing of the throughput rate, can be related to changes in the shape of the potential function of the node. The methodology of deriving the potential function of the node from its gradient dynamics and dynamic flow conservation considerations is presented. Using the results from catastrophe theory, it is shown that the abrupt changes in the throughput can be expected due to the existence of a catastrophe point in the parameter space. The behavior of a node in a homogeneous network can be characterized by a fold catastrophe. The simulation results are found to agree with the results obtained by the numerical method. >

On the behavioral aspects of alternate routing in non-hierarchical networks

Abstract The behavior of a node under alternate routing scheme in a homogeneous non-hierarchical network is modeled with respect to the equilibrium states. Under high load intensities, there exist two equilibrium states: one stable and the other unstable. The blocking probability at the stable equilibrium state is higher than that at the unstable one. The evolution of the perturbed system can be found to be dictated by two Liapunov functions. Under one of the Liapunov functions, the system evolves towards the normal state whereas under the other, the system evolves towards the congestion state . Congestion manifests owing to the fold catastrophe in the behavior manifold of the system. Simulation studies indicate that, at certain range of load intensities higher than the rate at the fold point, the throughput exhibits large fluctuations. These fluctuations are interpreted to be resulting from the dynamics of the system specified by the potential function of the system. A performance index, called the Sojourn Ratio (SR), characterizes the behavior of the system beyond the fold point. The ratio SR:(1-SR) is an estimate of the ratio of the duration in which the system is in the domain of the congestion state, to that in which it is in the domain of the normal state. We conjecture that the durations in which the system is in the normal state and in the congestion state are approximately proportional to the height of the potential barriers at the respective states. Accordingly, an analytically obtainable performance index V SR is defined as the ratio of the potential barrier at the congestion state, to the sum of the potential barriers at the normal state and congestion state. Among the characterizations of the system by Maxwell convention, by delay convention and by V SR , it is found that the last one captures best the tendency of SR.

On the structural uniqueness of alternate routing schemes in non-hierarchical networks

The authors examine the structural relationship between load and blocking probability for a fully connected homogeneous nonhierarchical network when blocked messages cause retrial and when different alternate routing strategies are employed to overcome congestion. The model employed for analysis is based on the flow approximation. It is found that retrials push the stable equilibrium state away from the zero blocking state, thereby aggravating congestion. The alternate routing strategies accommodate the stable equilibrium state close to the zero blocking state. However, both the retrials and the alternate routing strategies do not alter the fundamental structure of the system, namely, the fold catastrophe. By solving the degenerate equation, the value of appropriate control parameters can be obtained. According to the present model, it is only under schemes with no alternate routing that the system attains stability, in the mathematical sense of the term.<<ETX>>

A copy network with shared buffers for large multicast ATM switches

A new architecture for the copy network which is an integral part of multicast asynchronous transfer mode (ATM) switches is proposed. The new architecture makes use of the property that the Broadcast Banyan Network (BBN) is non-blocking if the active inputs are cyclically concentrated and the outputs are monotone. In the new architecture, by employing a token ring reservation scheme, the outputs of the copy network are reserved before a multicast cell is replicated. By the new copy principle, the number of copies requested by a multicast call is not limited by the size of the copy network, so that very large multicast switches can be configured in a modular fashion. The sequence of cells is preserved in the new structure. Though physically separated, buffers within the copy network are completely shared, so that the throughput can reach 100%, and the cell delay and the cell loss probability can be made very small.<<ETX>>

Performance and stability aspects of congestion control by input buffer limiting in store and forward networks

Store-and-forward techniques in computer communication networks are addressed. The performance estimation and the stability aspects of an input buffer limiting (IBL) scheme are presented. The model is formulated with respect to the state-dependent effective input rate and effective service rate. The computation of the performance parameters with respect to the effective service rate yields satisfactory results when blocking probabilities are not restricted to very low values (<<1). The stability aspects are assessed with the results from catastrophe theory; the stability is characterized as fold catastrophe. It is seen that, at higher rates of input, this maximum value of the IBL ratio approaches the capacity law limit proposed by S. Lam and M. Reiser (1979). Further, this method also approximately indicates the no-congestion region.<<ETX>>