Bernoulli Arrivals Research Articles

Analysis of packet switches with input and output queuing

A single-stage nonblocking N*N packet switch with both output and input queuing is considered. The limited queuing at the output ports resolves output port contention partially. Overflow at the output queues is prevented by a backpressure mechanism and additional queuing at the input ports. The impact of the backpressure effect on the switch performance for arbitrary output buffer sizes and for N to infinity is studied. Two different switch models are considered: an asynchronous model with Poisson arrivals and a synchronous model with Bernoulli arrivals. The investigation is based on the average delay and the maximum throughput of the switch. Closed-form expressions for these performance measures are derived for operation with fixed size packets. The results demonstrate that a modest amount of output queuing, in conjunction with appropriate switch speedup, provides significant delay and throughput improvements over pure input queuing. The maximum throughput is the same for the synchronous and the asynchronous switch model, although the delay is different. >

Design of an Optimum Channel Utilisation Multiaccess Protocol for Packet Radio Networks

Design and throughput performance of an Optimum Channel Utilisation Multiaccess (OCUM) protocol applicable to Packet Radio Networks (PRN) is presented in this paper. The OCUM protocol utilizes a slotted message channel for data transmission and a busytone channel for sensing and acknowledgement functions. The messages constitute multiple data packets where each packet length is equal to one slot size. The OCUM protocol design results in effective utilisation of the message channel by achieving minimum channel idle rate and collision rate. The throughput performance of the protocol has been analyzed for a finite population model with Bernoulli arrivals at cach node, geometric distribution of message lengths (measured in number of packets) and with no buffer assumption. Both the analytical and simulation results show that the protocol enjoys better throughput characteristics at high values of average message lengths making it ideally suited for file transfer type applications.

Closed-loop control with delayed information

The theory of Markov Control Model with Perfect State Information (MCM-PSI) requires that the current state of the system is known to the decision maker at decision instants. Otherwise, one speaks of Markov Control Model with Imperfect State Information (MCM-ISI). In this article, we introduce a new class of MCM-ISI, where the information on the state of the system is delayed. Such an information structure is encountered, for instance, in high-speed data networks. In the first part of this article, we show that by enlarging the state space so as to include the last known state as well as all the decisions made during the travel time of the information, we may reduce a MCM-ISI to a MCM-PSI. In the second part of this paper, this result is applied to a flow control problem. Considered is a discrete time queueing model with Bernoulli arrivals and geometric services, where the intensity of the arrival stream is controlled. At the beginning of slot t +1, t =0,1,2,…, the decision maker has to select the probability of having one arrival in the current time slot from the set { p 1 , p 2 }, 0 ≤ p 2 < p 1 ≤ 1, only on the basis of the queue-length and action histories in [ 0, t ]. The aim is to optimize a discounted throughput/delay criterion. We show that there exists an optimal policy of a threshold type, where the threshold is seen to depend on the last action.

Simultaneity in discrete-time single server queues with Bernoulli inputs

In discrete-time systems, arrivals and departures occur simultaneously. The present work focuses on the scheduling of arrivals and departures in discrete-time queues with Bernoulli arrivals and general independent service times. Both finite and infinite capacity queues are analysed. The waiting-room management policy takes care of the simultaneity problem. Two waiting-room management policies, AF (Arrivals First) and DF (Departures First) are singled out and their influence on the derivation of the state probabilities is investigated. Furthermore, the outside observer's distribution is shown to be identical to the arriving customer's distribution in the AF queue and a formula relating both distributions is provided for the DF queues.

Analysis of interdeparture processes for bursty traffic in ATM networks

Admission control in asynchronous transfer mode (ATM) networks is considered. An ATM switch is modeled as a discrete-time single-server queue at which the following three different kinds of arrival processes are allowed to join together: arrivals of cells with a general interarrival time distribution; Bernoulli arrivals of cells in batches; and interrupted Poisson processes. An exact analysis is given to derive the waiting-time distributions and interdeparture-time distributions for arriving cells subject to admission control in ATM networks. The model is extended to approximately obtain the end-to-end delay distributions for the designated traffic stream. Such an analysis is important for voice or coded video because they require a playout mechanism at the destination. Since the analysis is approximate, the simulation results needed to assess its accuracy are provided. Numerical examples show how the traffic characteristics of the designated traffic stream are affected by the total traffic load at the switching node, the number of other bursty traffic sources, and the degree of burstiness of the traffic source itself. >

On the Geo/D/1 and Geo/D/1/n queues

A discrete-time single server FIFO queue with Bernoulli arrivals and deterministic service times is studied. Both the finite capacity queue and the infinite capacity queue are investigated. The state of the system is observed at entry time and at the end of an arbitrary time slot. The closed-form expressions for the steady-state distributions of the queue length and of the unfinished work in system (i.e. waiting time) are obtained. The method of analysis, using Lindley's equation, naturally arises in case of deterministic service times.

Matrix-geometric solution for two node tandem queueing systems with phase-type servers subject to blocking and failures

This paper considers a two node tandem queueing system with phase-type servers and Bernoulli arrivals where the servers operate in discrete-time and are subject to blocking and failures. The invariant probability vector of the underlying finite state Quasi-Birth-and-Death process is shown to admit a matrix-geometric representation for all values of the arrival parameter λ. The corresponding rate matrix is given explicitly in terms of the model parameters and the resulting closed-form expression provides the basis for an efficient calculation of the invariant probability vector. The cases and 1 are studied separately and the irreducibility of the underlying Markov chain is investigated in each situation. The continuous-time formulation is briefly discussed and only major differences with the discrete-time results are pointed out. Some numerical examples are also provided

Buffer size for data communications over fading radio links

With the increasing importance of computer traffic over radio channels, it is important to study the effect of signal fluctuation. This paper is the first analysis of buffer requirements for retransmission error control schemes operating over fading links. It contains four principal contributions: design curves are presented for buffer size in terms of traffic and channel parameters; an intermittent server model for the channel is introduced and verified by simulation; transforms are found which give very tight approximations to buffer overflow and lost traffic probabilities for independent arrivals pattern and a semi-Markov server; and finally, an exact analysis of Bernoulli arrivals is presented and assessed as an easily calculated approximation to more general arrival patterns.