Probability Distribution Of Delay Research Articles

The accuracy of multicanonical system models

We compare the precision of two multicationical iteration techniques in communication system modeling though an analysis of the differential group delay probability distribution in a multisection polarization emulator.

Measuring Recurrent and Nonrecurrent Traffic Congestion

A methodology and its application to measure total, recurrent, and nonrecurrent (incident related) delay on urban freeways are described. The methodology used data from loop detectors and calculated the average and the probability distribution of delays. Application of the methodology to two real-life freeway corridors in Los Angeles, California, and one in the San Francisco, California, Bay Area, indicated that reliable measurement of congestion also should provide measures of uncertainty in congestion. In the three applications, incident-related delay was found to be 13% to 30% of the total congestion delay during peak periods. The methodology also quantified the congestion impacts on travel time and travel time variability.

Performance of Bluetooth Slave/Slave Bridge

The performance of a Bluetooth scatternet with a Slave/Slave bridge is analyzed using the tools of queueing theory. We analyze two possible scheduling policies: limited service and exhaustive service, and derive analytical results for the probability distribution of access delay (i.e., the time that a packet has to wait before being serviced) and end-to-end delay for both intra- and inter-piconet bursty traffic. The exhaustive service discipline was found to provide lower values for all delay variables, over a wide range of parameter values. All analytical results have been confirmed through simulations.

Multicanonical communication system modeling-application to PMD statistics

The authors extend multicanonical sampling to the determination of probability density functions in communications systems. The resulting easily programmed iterative procedure generates the probability of both frequent and rare events with equivalent accuracy. The applicability of the technique is verified through a calculation of the differential group delay probability distribution in a multisection polarization emulator.

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: application to the time-delay problem.

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.

Performance analysis of CFDAMA-PB protocol for packet satellite communications

Combined free/demand-assignment multiple-access (CFDAMA) schemes are suitable for broad-band packet satellite communications systems serving a finite number of bursty data sources. The performance analysis of the CFDAMA using piggy-backed (PB) reservation is presented. The probability generating function (PGF) of the packet delay is developed. The performance is evaluated in terms of three performance measures: average packet delay, variance of packet delay, and cumulative probability distribution of packet delay. Performance comparison with other pertinent schemes shows CFDAMA-PB to be superior for a wide range of user population sizes.

A MAC protocol for HFC networks: Design issues and performance evaluation

Medium Access Control (MAC) layer protocols are designed to control transmissions over shared mediums. Bi-directional Cable TV networks using Hybrid Fiber/Coazial (HFC) systems are good examples of broadcast environments where a MAC protocol is needed to allocate the multiaccess medium among the various nodes. One can think of a MAC protocol as a collection of components each performing a certain number of functions. An HFC MAC protocol can be broken into the following set of components: ranging or acquisition process, frame format, support for higher layer traffic classes, bandwidth allocation, bandwidth request, contention resolution mechanism. Ranging is the phase during which the round trip delay time to the head-end is calculated and the station synchronization to the downstream timing is performed. The frame format element of the MAC defines the upstream and downstream frames and describes their contents. If the MAC needs to provide support for ATM, it also needs to differentiate between different classes of traffic supported by ATM, such as Constant Bit Rate (CBR), Variable Bit Rate (VBR) and Available Bit Rate (ABR). Bandwidth allocation represents an essential part of the MAC and controls the granting of requests at the headend. Finally, the contention resolution mechanism which is maybe the most important aspect of the MAC consists of a backoff phase and a retransmission phase. This paper examines two of the MAC elements mentioned above, namely the contention resolution and the bandwidth allocation mechanisms. Different solutions for each component are considered and evaluated. Performance is measured in terms of request delay, mean access delay and access delay probability distribution. Simulation results for configurations and scenarios of interest are also presented.

Analytic evaluation of contention protocols used in distributed real-time systems

The probability of a station failing to deliver packets before their deadlines, called theprobability of dynamic failure, P dyn, is an important measure for the communication subsystem of a distributed real-time system. Another closely-related performance measure is the ε-bounded delivery time,T ε, which is defined as the least time needed to deliver a packet with probability greater than 1−ε. UsingP dyn andT ε, we comparatively evaluate four contention protocols often used in distributed real-time systems: (i) the token passing protocol and its priority-based variation (called thetoken scheduling protocol), and (ii) theP i-persistent protocol and a priority-based variation thereof. The communication subsystem equipped with different contention protocols is modeled first as embedded Markov chains. Then, we derive the probability distributions of access delay, from whichP dyn andT ε can be calculated. The blocking probability,Q i, can also be derived from the access delay distribution. These measures are derived first under the assumption of a single buffer at each station. The single-buffer model is then extended to the multiple-buffer case. The effects of buffer size onP dyn,T ε, andQ i, and the performance improvement with multiple buffers are analyzed over a wide range of network traffic.

Modeling probability distribution of delay at signalized intersections

AbstractAccurate estimation of vehicle delay is difficult because of the randomness of traffic flow and large number of factors affecting intersection capacity. Existing delay models simplify the real traffic conditions and provide only approximate point estimates of average delay, whereas its variability should also be of interest. A stochastic model was used to study the changing probability distribution of delay. The model is based on sequential calculation of queue length probabilities with any type of arrival process. Delay probability distribution was investigated for different degrees of saturation, arrival types and control conditions. The variance of delay increases rapidly with degree of saturation and is inversely proportional to the approach capacity. Other parameters such as cycle time and saturation flow do not have a significant effect on delay distribution. Both the mean and variance of delay are sensitive to arrival process characteristics and increase with the variance of arrivals.

Derivation and application of hard deadlines for real-time control systems

A method for calculating the hard deadlines in linear time-invariant control systems by considering system stability and the allowed state-space is presented. To derive necessary conditions for asymptotic system stability, the state difference equation is modified based on an assumed maximum delay and the probability distribution of delays whose magnitudes are less than, or equal to, the assumed maximum delay. The allowed state-space-which is derived from given input and state constraints-is used to calculate the hard deadline as a function of time and the system state. A one-shot delay model in which a single event causes a dynamic failure is considered. The knowledge of hard deadline is applied to the design of error recovery in a triple modular redundant controller computer. >

Gravitational lensing, time delay, and gamma-ray bursts

The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. For point lenses (all with the same mass) the probability distribution is broad, and with a peak at delta(t) of about 50 S; for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median delta(t) equals about 1/h month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of 'recurrent' bursts due to gravitational lensing by galaxies is probably between 0.05 and 0.4 percent. Gravitational lensing can be used as a test of the cosmological origin of gamma-ray bursts.

Headstart Strategies for Combating Congestion

When a traveler, or other user of a congested system, wishes to be reasonably sure of reaching a destination, or finishing a task, on time he must start early enough to compensate for random delays. This paper investigates the headstart decision policy arising if costs are attached both to lateness and to an otherwise undesirable early departure. The model encompasses a case in which the probability distribution of congestion delays is unknown, and must be inferred from previous experience.

Probability Distribution of Delays for Store-and-Forward Traffic Mixed with Direct Traffic

This paper discusses the delay probability distributions of store-and-forward (S/F) traffic sent over the same trunks as direct traffic. The operating principles for mixing are the same as described in a previous paper, i.e., the S/F traffic is held back until the trunk group is not congested with the direct traffic: a specified number of trunks are held in reserve for the possible arrivals of direct traffic. In this study, only that portion of the total S/F message delay caused by the presence of the direct traffic on the trunks is investigated. The effect that the S/F traffic has on the distribution of delays is assumed negligible. Because of this assumption, the results apply when the load of the S/F traffic is small compared to direct traffic or, when the load of S/F traffic is appreciable, the results apply to a small portion of the S/F traffic which, because it enjoys the privilege of priority, is placed at the head of the queue. A method of computation and some specific results are presented. The numerical results are for trunk groups of from 2 to 48 trunks. Exponentially distributed holding times of the direct traffic are assumed.