A study of a time dependent queueing system with two parallel channels

A time dependent queueing system is studied by obtaining the probabilities of the exact number of arrivals and departures by a given time. The service is accomplished through two parallel channels, each channel having a different service rate. The marginal probability of exactly i arrivals and the mean number of i arrivals are obtained.     

Calculation of message length transition probabilities in selectivereject ALOHA channels

A method is described for the exact calculation of message length transition probabilities in asynchronous selective reject (SREJ) ALOHA channels with Poisson message arrivals. The formulas derived are used for exact calculation of the throughput characteristics of example SREJ-ALOHA channels which were previously analyzed using bounds or approximate methods     

A queueing problem with random memory arrivals and heterogeneous servers

This paper studies the steady state behaviour in discrete time of a limited space queueing problem with random memory arrivals wherein service is accomplished through S-heterogeneous parallel channels. The arrivals at two consecutive time marks depend upon a random variable which takes values one and zero with probabilities p and q respectively according to whether the arrivals at two consecutive time marks are correlated or uncorrelated. The explicit probabilities for the number of units in the system have been worked out. Some special cases of interest have also been derived.     

Analysis of a discrete-time queue with integrated bursty inputs in ATM networks

In this paper, we carry out an exact analysis of a discrete-time queue system with a number of independent Markov modulated inputs in ATM networks, using a generating function approach. We assume that the queueing system has an infinite buffer with M servers. The cell arrival process is characterized by a number of independent Markov modulated geometrical batch arrival processes. We first obtain the generating function of the queue-size distribution at steady-state in vector form, then derive an expression for the average queue-size in terms of the unknown boundary probabilities. To obtain those unknown probabilities, we use the technique proposed in Reference 1. This involves decomposing the system characteristic function to evaluate the roots and solving a set of linear equations. One of the contributions of this paper is presented in Lemma 1, which characterizes the property of the underlying eigenvalues. For one special case of at least M-1 cell arrivals during one slot at one Markov state and of at least M arrivals at all other states, the determination of the unknowns is straightforward. If every Markov modulated arrival process can be further decomposed into a number of i.i.d. two-state, or three-state, or even four-state Markov modulated arrival processes, then each root can be obtained separately using an iterative algorithm. Numerical results are presented to validate the proposed traffic models against actual traffic measurements.     

Loss probabilities for messages with redundant packets feeding afinite buffer

The purpose of this paper is to obtain the distribution of the number of lost packets within a sequence of n consecutive packet arrivals into a finite buffer M/M/1 queue. We obtain explicit expressions for the multidimensional generating function of these probabilities based on a recursive scheme introduced by Cidon et al. (1993). We then analyze the loss probabilities of a whole message, and analyze the effect of adding redundant packets. We show that in both heavy traffic as well as in light traffic conditions, adding redundant packets results in decreasing the message loss probabilities     

On the Delay Analysis of a TDMA Channel with Finite Buffer Capacity

The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.     

ATM network traffic characterization using two types of on–off sources

An approximate model for characterizing aggregated cell arrivals from heterogeneous sources to an ATM multiplexer is proposed. The model consists of two types of on–off sources and provides enough degrees of freedom to match a number of moments of cell arrival rates as well as the time correlation of the aggregated cell arrivals. Numerical results indicate that the queue length distributions obtained using the model closely approximate the exact results.     

A Model for Telephone Networks and Its Use for Routing Optimization Purposes

The problem studied here concerns the modeling of call blocking in telephone networks. From the usual assumptions such as exponential arrivals and holding time, lost call cleared, the state of the network is described by a finite Markov chain. From the transition probabilities of this process are derived the differential equations associated with the average occupancy of all trunk groups. These traffic equations are simplified by considering independence of blocking for trunk groups in series. The blocking probabilities are estimated using fictitious offered traffic and the Erlang B formula. Such representation takes into account peaky or smooth traffic characteristics. We develop this one-moment model for routing policies such as load sharing and overflow routing. Performances of the model are given in comparison to the solution of the exact Markov chain model or the results of Monte Carlo simulation. Finally, an application to routing optimization and network dimensioning is treated.     

A new measure for time-dependent queueing systems with statistically dependent arrivals

This paper studies a first-come, first-served, queueing system wherein statistically dependent arrivals can occur only at the imaginary transition marks and statistically independent departures can occur at any point of time. Both intertransition times and service times are following the exponential distribution. Probability of exact number of arrivals and departures are obtained explicitly by solving the difference equations iteratively. Particular cases of interest are also derived therefrom.     

An M/M/1 ∞ queueing system with feedback

For a continuous time M/M/1 queueing system with feedback, explicit probabilities of exactly i arrivals and j departures and the marginal probabilities of exactly i arrivals and j departures are obtained by solving the difference equations recursively. Particular cases of interest are obtained.     

The effect of capture on performance of multichannel slotted ALOHAsystems

The author presents an exact analysis to evaluate the effect of capture on the multichannel slotted ALOHA protocol. The author derives the probabilities of the successful transmission. These probabilities are used to calculate the throughputs, average packet delays for both IFT (immediate-first-transmission) and delayed-first-transmission protocols and numerically compare the performance of the systems with and without capture. Numerical results show that when a quantitative capture restriction u is considered, in a multichannel system having a fixed total bandwidth, depending on parameter u and channel number M, an improved system performance such as the average channel utilization and average packet delay can be obtained     

Rare event analysis of batch-arrival queues

This paper deals with the analysis of small overflow probabilities in single-server queues with batch arrivals. First, for the class of GI ^X /G/1 queues we give analytical expressions for the decay rate (in the buffer size) of these probabilities. In case of Poisson arrivals, effective bandwidth results are deduced. Furthermore, we propose a change of measure which enables the execution of importance sampling in an asymptotically optimal way. Simulation results for a specific application show large speed-ups.     

Behavior of Tandem Buffers with Geometric Input and Markovian Output

A discrete-time system of infinite-capacity buffers in tandem is studied. The input process to the first buffer consists of individual arrivals characterized by a geometric distribution of the time between arrivals; and the probability that the output channel of each buffer, except the last, is transmitting at any epoch depends only on the number of digits in the buffer at that epoch. The transmitting state of the last buffer may depend more generally on the history of that buffer. The analysis shows that in equilibrium, the input processes to the subsequent buffers in the system are geometric with the same parameter as the input process to the first buffer. Therefore, each buffer in the system can be analyzed separately. Furthermore, the equilibrium state probabilities for a given buffer at a given epoch are independent of those for any other buffer in the system at the same epoch.     

Exact performance analysis of linear block codes in frequency-hopspread spectrum communication systems

We present a framework for determining the exact decoder error and failure probabilities for linear block codes in a frequency-hop communication channel with an arbitrary number of conditional symbol error and erasure probabilities. Applications are demonstrated for type-I hybrid ARQ systems by deriving equations for the packet error probability and throughput. Because these quantities are too small to be obtained by simulation, the framework provides exact results which are unobtainable by previous work     

A queueing system with stepwise randomly available additional space

In this paper we consider the steady state behaviour of a queueing system. The arrivals follow Poisson distribution and the service time distribution is exponential. Whenever the system size reaches a certain length, the system adds an additional space of unit size on every arrival with some probability and drops the additional space at the departure. Steady state probabilities are calculated explicitly and the average number of customers in the system is also obtained. Associating the cost with the rent of the additional space and the profit with each customer served, a criterion to obtain the optimum size of the ordinary space and the optimum number of unit size additional spaces to be hired is discussed.     

An additional space special service facility heterogeneous queue

In this paper we consider steady-state behaviour of a heterogeneous queueing system with instantaneously available special service facility and probabilistically available additional space both of which are queue-length dependent. The system operates at two different levels. The arrivals and the departures at these two levels occur at different rates. Steady-state probabilities at both the levels are calculated explicitly. Average number of customers in the system is also obtained. Associating the various costs, a criterion to obtain the decision points at which the hiring of additional space will be profitable and that for the size of additional space to be hired is discussed.     

On error probabilities of DS-CDMA systems with arbitrary chipwaveforms

The error probabilities of asynchronous DS-CDMA systems using random signature sequences depend on the number of users, the processing gain and the chip waveforms employed. The exact calculation of the error probabilities is computationally difficult and therefore approximations and bounds are more commonly used. In this article, the improved Gaussian approximation proposed by Holtzman (1992) is extended to include arbitrary chip waveforms. Comparisons to the exact calculation and the standard Gaussian approximation are also made to evaluate the accuracy of the improved Gaussian approximation     

On the Calculation of Overflow Systems with a Finite Number of Sources and Full Availiable Groups

This paper deals with the calculation of loss probabilities in overflow systems with a finite number of sources and full available groups. An exact, explicit solution is derived for overflow systems with only one primary group. Furthermore, an exact method is applied in case of overflow systems with two primary groups. For overflow systems with an arbitrary number of primary groups an approximate method is developed which takes into account the variance of offered overflow traffic. This approximate method yields results which are in good agreement with exact calculations and simulation results.     

Analysis of interdeparture processes for bursty traffic in ATMnetworks

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     

Parameter estimation for partially observed queues

We consider parameter estimation for a FIFO queue with deterministic service times and two independent arrival streams of “observed” and “unobserved” packets. The arrivals of unobserved packets are Poisson with an unknown rate λ while the arrivals of observed packets are arbitrary. Maximum likelihood estimation of λ is formulated based on the arrival times and waiting times of k observed packets. The likelihood function is derived in terms of the transition probabilities of the unfinished work process which are calculated recursively. Sufficient conditions for consistency, asymptotic normality, and asymptotic efficiency are given. The mean and variance of the MLE are measured in simulation experiments. Numerical results indicate that the MLE is consistent and asymptotically normal