General probability density function of packet service times for computer networks

The letter presents derivations of a generalised probability density and distribution functions of packet service times for computer communication networks. Included in the derivation are the effects of message segmentation into packets and the effects of control traffic. We also present the first and the second moments of the packet service times. These expressions can be used in modelling and analysis of computer networks by assigning appropriate values to various parameters.     

Message Delay Analysis for Polling and Token Multiple-Access Schemes for Local Communication Networks

Two efficient polling (token) schemes, which provide multiaccess coordination for local area networks, are described, analyzed, and compared. The two multiple-access polling protocols described here utilize gated and exhaustive disciplines in ordering the transmission of the messages buffered at each terminal. The delay-throughput performance behavior of polling schemes operating under the above mentioned disciplines is derived. Network terminals are modeled as independent sources, which generate messages in accordance with a renewal process. A queueing theoretic approach is employed in deriving the actual message delay. behavior of both schemes. Several comparisons are presented. Interesting results are obtained when we compare the average message waiting times in the case when the network traffic is completely balanced with the ease when this same traffic is mostly due to a single node. The latter case would arise, for example, m networks employing gateways.     

Approximation to expected message delay of polling systems

The author discusses polling systems with single message queues and asymmetric exponential arrivals. A simple method is presented to obtain both an upper bound on the cycle length and an approximation to the expected message delay of these polling systems. Numerical examples show that the approximation obtains results which are very close to the simulation results     

Location update cost of distance-based scheme for PCS networks with CTRW model

This letter concerns the optimization of the dynamic location-update area (LA) for the per-user distance-based scheme in personal communication service (PCS) networks. We have two main contributions: (1) under the general and popular one-dimensional (1-D) continuous-time random walk (CTRW) mobility model, we propose a novel framework to analyze the location update cost; (2) with this framework, we investigate the impact of call arrivals and the initial position of the mobile terminal (MT) on the position of the LA, which was neglected by previous work. Simulation shows that our theoretical model is very accurate.     

The Behavior of a Finite Queue with Batch Poisson Inputs Resulting from Message Packetization and a Synchronous Server

This paper studies the behavior of a packet switch which provides finite waiting space and receives packetized messages. The arrivals of the messages constitute a Poisson process. Each message consists of a random number of packets. The number of packets contained in a message is assumed to be an integer-valued random variable which may follow any arbitrary probability distribution. All packets residing in the buffer receive service from a single output transmitter operating synchronously at a constant rate. Each packet receives the same fixed service time from the transmitter and then leaves the system. Upon the arrival of a message, if the remaining buffer space is not enough to accommodate all packets of the message, then the entire message is completely rejected. Results such as message blocking probability, packet blocking probability, throughput, and mean delay have been obtained. Two different approaches, minislot approximation and the application of the residue theorem, are used to obtain these results. Especially, this combinatorially very complex problem is successfully solved by the residue theorem in a recursive manner. These results are useful in evaluating the performance of a packet switch. They are also useful for design purposes.     

Performance of the timed token scheme in MAP

Two new analytic approximations are given for the mean delay in the timed token bus network specified in MAP (manufacturing automation protocol). Each station on the network has two kinds of timer for controlling the maximum amount of time for data transfer before giving up the token. High-priority stations would set large values in the token holding timer (THT) and transmit until the timer expires. Low-priority stations compare the elapsed time since the last token arrival (measured cycle time) to the token rotation timer (TRT) setting, and transmit only for the time left in the timer. The first approximation, based on Fuhrmann's bound for the limited-k service discipline, is for the symmetric case where all the stations have the same traffic load and the identical THT or TRT settings. The approximation has been compared to simulation results, and found to be quite accurate for a representation factory network, with THT or TRT set at two and five times the average total walk time. The second approximation is for the asymmetric case where there is one saturated low-priority (limited-TRT) station, and the rest of the stations in the network have high priority with limited-THT service. These two formulas will be useful in the planning and operation of MAP networks by providing guidance in the choice of timer settings for meeting different priority service requirements     

Output moments and photon statistics in fiber raman amplification

The problem of output moments, photon statistics, and signal-to-noise ratio in fiber Raman amplification is considered using a master equation approach, including absorption in the signal and pump modes. In the parametric approximation for the pump, results are obtained for the output moments which can be cast in a general form derived by Loudon and Shepherd [23] for phase-insensitive quantum amplifiers and attenuators. Beyond the parametric approximation, it is shown that the output moments of the signal may be obtained through iteration from lower order moments in an approximation where signal-pump correlation is ignored. Comparison with other work is discussed.     

Multipoint Private Line (MPL) Access Delay Under Several Interstation Disciplines

A multipoint private line (MPL) network is designed to operate within specified system-performance objectives. Performance objectives for some types of computer-communications networks are stated in terms of access-delay statistics which measure the grade of service experienced by the stations bidding for access to the private line. Access delay is defined to be the time from when a message reaches the head of its queue at the station-and no message from its queue is being processed-until transmission of the message begins. Using simulation and some analysis, we examine and compare the access delay statistics for an MPL circuit under each of four possible service disciplines for the stations on the circuit. The results in this paper have proven useful in designing certain types of MPL networks for a variety of system parameters.     

Approximate analysis of asymmetric single-service token-passingsystems

Consideration is given to token-passing or polling systems in which the message arrival process, the message transmission time distribution, and the walk time vary from one station to another. An approximate analysis of these systems is obtained. The results obtained from the approximate analysis are compared against both simulation results and those obtained from two approximate methods that have been proposed earlier. For the special case of a symmetric system, it is shown that the approximate analysis is exact when the walk time is constant. Even when the walk time is exponentially distributed, it is shown that the approximate analysis gives an approximation error of less than 0.3% in the range of offered load that is generally of interest     

Waiting time estimates in symmetric ATM-oriented rings with thedestination release of used slots

This paper considers the basic access mechanism in asynchronous transfer mode (ATM)-oriented rings which, like Orwell, ATM ring, and ALine, apply destination release of used slots. The released slots may be reused by the destination station, or in some protocols, they must be given to the next station. Such a mechanism can be modeled by a multiple-server multiqueue system, where switchover times between consecutive polling instants of the queues are nonzero. The server polls the queues according to a certain polling discipline, which is dependent on the service time. This paper presents approximate mean minipacket waiting times in such systems. The approximation is based on a polling queueing model with Markovian server routing. Poisson arrivals and a symmetric workload model for minipackets having a full and partial traffic matrix are assumed. The performance characteristics are compared between the alternative options     

Performance Analysis for a Terminal-Priority Contentionless Access Algorithm for Multiple-Access Communications

We consider a multiple-access broadcast communication channel which serves a network of terminals, each characterized by a distinct priority level. Higher priority terminals require, on the average, faster access across the communication channel than lower priority ones. We present a terminal priority contentionless access (TPCA) control scheme for sharing such a channel on a conflict-free basis. A ready terminal wishing to access the channel will wait for the channel to become idle, and then defer its access untill after higher priority terminals are given the opportunity to transmit. The model accounts for acquisition delays (including propagation and timearound delay components), idle detection times, multipacket message structures and different arrival intensities at different terminals, Analytical results are derived for the moments and transform of the message waiting-time distribution at each network terminal by relating the waiting times in our model to those in an appropriateM/G/1queue with HOL (head of the line) priorities. Performance curves are presented under varirous system parameter conditions which correspond to applications involving digital radio local distribution systems and metropolitan-area, packet radio, and local-area communicatiton networks.     

Centralized Wireless Data Networks With User Arrivals and Departures

A dynamic-user model for centralized wireless networks is studied, where users arrive with a certain file size and depart when the file is served by a central server. Although the exact analysis of dynamic-user systems can be complicated, it is shown that an approximate analysis can be performed in a time-scale separation regime where the file size is much larger than the time scale of service process fluctuation. A first-order approximation result is derived that shows that when file sizes are large, a complicated service process can be replaced by a simple constant-rate service process. The accuracy of the approximation is further improved through a second order approximation result that incorporates the effect of service variability. Variability in the service process is shown to reduce the effective service rate, leading to a quantification of the conventional heuristic that service variability degrades system performance     

L’indiscernabilité locale dans les réseaux de files d’attente à multiliaisons ou multiserveurs

As previously for single link queueing networks, now it is proved, for multiserver (multilink) queueing networks, that the local queues are defined byindistinguishable local arrivals (after having crossed two or three stages), corresponding (in buffers) to someagglutinations of short service times behind long service times, possibly leading (in the input buffers) to very long congestion times (even for low traffic intensities)when the service times are highly varying. In that case, traditional queueing theories (mainly influenced by the loads) are not appropriate for input buffer dimensioning.     

An M/G/1-type queueing system with non-perfect servers and no waiting capacity

A single server queue with Poisson arrivals and no waiting room is considered where two types of services are offered. An arriving customer has to undergo the first service but the second service is optional. The service times for both types of services are exponentially distributed. Transient and steady-state distributions have been obtained for the number in the system.     

Joint distribution of numbers of location updates and cell boundary crossings in movement-based location management schemes

The movement-based location management (LM) scheme is a well-known dynamic LM scheme that is relatively easy to implement. In this letter, we derive the joint probability distribution of the number of cell boundary crossings and number of location updates of a mobile terminal, assuming Poisson call arrivals and generally distributed cell residence time, under movement-based LM. The derived movement statistics are used to bound the movement threshold so that the number of location updates is kept within a reasonable range. Numerical results are presented.     

Analytic approximation of the jitter incurred by CBR traffics in IP networks

In this paper, an analytic approximation is derived for the end-to-end delay-jitter incurred by a periodic traffic with constant packet size. The single node case is considered first. It is assumed that the periodic traffic is multiplexed with a background packet stream under the FCFS service discipline. The processes governing the packet arrivals and the packet sizes of the background traffic are assumed to be general renewal processes. A very simple analytical approximation is derived and its accuracy is assessed by means of event-driven simulations. This approximation is then extended to the multiple node case yielding a simple analytical approximation of the end-to-end jitter. This approximation is shown to be fairly accurate in the light to moderate traffic conditions typically encountered in IP core networks.     

Signal selection in communication and radar systems

A criterion for selecting a finite set of transmitter signals for a continuous communication channel is proposed. The "optimum" signal sets using this criterion are selected to maximize the minimum divergence between hypothesis pairs being tested at the receiver. The resulting signal sets have the property that the error probability using these signals is less than the error probability for any other choice of signals for some {em a priori} message statistics. The signal selection procedure may be applied without a knowledge of the {em a priori} message statistics and does not require an evaluation of error probabilities. Four examples of signal selection are included to illustrate the procedure.     

Two-class priority queueing system with restricted number of priority customers

In this paper, we analyze a two-class single-server preemptive priority queueing system with arrivals to each class are assumed to follow a Poisson process with exponentially distributed service times. Customers are served on a first-come, first-served basis within their own queue. Explicit expressions for the mean queue length and the steady-state joint distribution of the number of high and low priority customers in the system are derived. The analysis is based on the generating function technique. The obtained expressions are free from Bessel functions or any integral functions. Moreover, numerical values testing the quality of our analytical results are also presented.     

Moments of a filtered binary process (Corresp.)

The problem of determining the moments of the output of a resistance-capacitance (RC) filter driven by a random binary process is considered. It is assumed that the driving process is governed by an alternating renewal process. A method is given for computing the moments of any order, as well as the conditional moments and moments of the local maxima and minima. Explicit formulas are given for the second moment in the asymmetric case and second and fourth moments in the symmetric case.     

A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It constitutes a throughput-critical task at the medium access control layer of today's wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportunistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized channel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.