Efficient parallel simulation of a sliding window protocol

This paper is concerned on an M/M/1 queue with correlated interarrival and service times. In particular, we assume that the interarrival time and service time of a customer have a bivariate exponential distribution. By utilizing a Markov modulated fluid flow (MMFF) process associated with the age process of the customer in service, we obtain a number of queueing quantities in closed form. Using the solutions, the impact of the correlation coefficient of the interarrival and service times on a variety of queueing quantities is explored quantitatively and qualitatively. Specifically, we establish a monotonic relationship between the decay rates of queueing quantities and the correlation coefficient of the interarrival and service times. We also show that the decay rates are increasing in the correlation coefficient. In addition, queues with the maximum/minimum correlation coefficient are analyzed. Two examples are presented to demonstrate the importance of using the correlation coefficient in queueing performance/economic analysis.

A parallel prefix circuit takes n inputs x 1, x 2, ..., x n and produces the n outputs x 1, x 1 ∘ x 2, ..., x 1 ∘ x 2 ∘ ⋯ ∘ x n , where’∘’ is an arbitrary associative binary operation. Parallel prefix circuits and their counterparts in software, parallel prefix computations or scans, have numerous applications ranging from fast integer addition over parallel sorting to convex hull problems. A parallel prefix circuit can be implemented in a variety of ways taking into account constraints on size, depth, or fan-out. Traditionally, implementations are either defined graphically or by enumerating the underlying graph. Both approaches have their pros and cons. A figure if well drawn conveys the possibly recursive structure of the scan but it is not amenable to formal manipulation. A description in form of a graph while rigorous obscures the structure of a scan and is equally hard to manipulate. In this paper we show that parallel prefix circuits enjoy a very pleasant algebra. Using only two basic building blocks and four combinators all standard designs can be described succinctly and rigorously. The rules of the algebra allow us to prove the circuits correct and to derive circuit designs in a systematic manner.

Existing ad hoc routing protocols are either unicast or multicast. In this paper we propose a simple extension to the Dynamic Source Routing Protocol (DSR) to cater for group communications where all node addresses are unicast and there is no single multicast address. The proposed sliding window protocol results in significant improvement in total packet delivery. We also compare the group rekeying rate using the sliding window protocol versus other kinds of Rekeying algorithms. The proposed sliding window protocol performs better. The proposed sliding window is therefore simple and improves both communications and security performance.

Models are given for sequences of correlated exponential interarrival and service times for a single-server queue. These multivariate exponential models are formed as probabilistic linear combinations of sequences of independent exponential random variables and are easy to generate on a computer. Limiting results for customer waiting time under heavy traffic conditions are obtained for these queues. Heavy traffic results are useful for analyzing the effect of correlated interarrival and service times in queues on such quantities as queue length and customer waiting time. They can also be used to check simulation results.

In this paper we study a broad class of semi-Markovian queues introduced by Sengupta. This class contains many classical queues such as the GI/M/1 queue, SM/MAP/1 queue and others, as well as queues with correlated inter-arrival and service times. Queues belonging to this class are characterized by a set of matrices of size m and Sengupta showed that its waiting time distribution can be represented as a phase-type distribution of order m. For the special case of the SM/MAP/1 queue without correlated service and inter-arrival times the queue length distribution was also shown to be phase-type of order m, but no derivation for the queue length was provided in the general case. This paper introduces an order m^2 phase-type representation (kappa, K) for the queue length distribution in the general case. Moreover, we prove that the order m^2 of the distribution cannot be further reduced in general. Examples for which the order is between m and m^2 are also identified. We derive these results in both discrete and continuous time and also discuss the numerical procedure to compute (kappa, K). Moreover, by combining a result of Sengupta and Ozawa, we provide a simple formula to compute the order m phase-type representation of the waiting time in a MAP/MAP/1 queue without correlated service and inter-arrival times, using the R matrix of a Quasi-Birth-Death Markov chain.

A matrix geometric representation for the queue length distribution of multitype semi-Markovian queues

The problem of digit set conversion for fixed radix is investigated for the case of converting into a non redundant, as well as into a redundant, digit set. Conversion may be from very general digit sets, and covers as special cases multiplier recodings, additions, and certain multiplications. We generalize known algorithms for conversions into non redundant digit sets, as well as apply conversion to generalize the O(log n) time algorithm for conditional sum addition using parallel prefix computation, and a comparison is made with standard carry-lookahead techniques. Examples on multi-operand addition are used to illustrate the generality of this approach. O(1) time algorithms for converting into redundant digit sets are generalized based on a very simple lemma, which provides a framework for all conversions into redundant digit sets. Applications in multiplier recoding and partial product accumulation are used as exemplifications.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We consider the stability of N-model systems that consist of two customer classes and two server pools. Servers in one of the pools can serve both classes, but those in the other pool can serve only one of the classes. The standard fluid models in general are not sufficient to establish the stability region of these systems under static priority policies. Therefore, we use a novel and a general approach to augment the fluid model equations based on induced Markov chains. Using this new approach, we establish the stability region of these systems under a static priority rule with thresholds when the service and interarrival times have phase-type distributions. We show that, in certain cases, the stability region depends on the distributions of the service and interarrival times (beyond their mean), on the number of servers in the system, and on the threshold value. We also show that it is possible to expand the stability region in these systems by increasing the variability of the service times (without changing their mean) while keeping the other parameters fixed. The extension of our results to parallel server systems and general service time distributions is also discussed.

This paper presents a general framework for optimal task reallocation in heterogeneous distributed-computing systems and offers a rigorous analytical model for the stochastic execution time of a workload. The model takes into account the heterogeneity and stochastic nature of the tasks' service and transfer times, servers' failure times, as well as an arbitrary task-reallocation policy. The stochastic service, transfer and failure times are assumed to have general, age-dependent (non-exponential) distributions, resulting in a tandem distributed queuing system with non-Markovian dynamics. Auxiliary age variables are introduced in the analysis to capture the memory associated with the non-Markovian stochastic times, thereby enabling a regenerative age-dependent analytical characterization of the statistics of the execution time of a workload. The model is utilized to devise task reallocation policies that optimize three metrics: the average execution time of a workload, the quality-of-service in executing a workload by a prescribed deadline and the reliability in executing a workload. Implications of the non-exponential event times on these metrics are also studied. Key results are verified experimentally on a distributed-computing testbed.

The average delay for the GI/G/1 queue is often approximated as a function of the first two moments of interarrival and service times. For highly irregular arrivals, however, it varies widely among queues with the same first two moments, even in moderately heavy traffic. Empirically, it decreases as the interarrival time third moment increases. For GI/M/1 queues, a heavy-traffic expression for the average delay with this property has been previously obtained. The method, however, sheds little light on why the third moment arises. We analyze the equilibrium idle-period distribution in heavy traffic using real-variable methods. For GI/M/1 queues, we derive the above heavy-traffic result and also obtain conditions under which it is either an upper or lower bound. Our approach provides an intuitive explanation for the result and also strongly suggests that similar results should hold for general service. This is supported by empirical evidence. For any given service distribution, it has been conjectured that the expected delay under pure-batch arrivals, where interarrival times are scaled Bernoulli random variables, is an upper bound on the average delay over all interarrival distributions with the same first two moments. We investigate this conjecture and show, among other things, that pure-batch arrivals have the smallest third moment. We obtain conditions under which this conjecture is true and present a counterexample where it fails. Arrivals that arise as overflows from other queues can be highly irregular. We show that interoverflow distributions in a certain class have decreasing failure rate.

The toll road service is planned and built to fund road construction and management of traffic operations. Although the toll service has several benefits, it also has challenges by creating a queue in the event of high traffic. Queues at a toll service in addition to pollution and waiting time costs also expose drivers to road traffic accidents and affect the economy of the country. Queuing problems at highway gates and exits due to toll service have become the main concern for transport managers and planners because of the randomness of inter-arrival and service time. The critical point in the management of toll road services is finding the optimal number of servers. This paper aims to analyze the queue feature to optimize the toll service using analytical and simulation models by considering the Addis-Adama expressway toll service in Ethiopia. The paper used a mathematical model and a simulation model using the CPN tools to investigate the queuing parameters. Then the model results helped us to get the optimum output by using economic analysis and identifying the minimum waiting time and operating cost without expense. The performance of the toll service highly depends on the number of servers, the number of vehicles in the system and queue, waiting time in the queue, service time, and inter-arrival time.

In the foreground of this work stands the question if communication should be understood as an interpretation process or as an instructional phenomenon. The interpretative view of communication is the one advocated by Shannon's classical communication model of 1949. This (technical) model has even penetrated the human sciences and is the base of todays computer communications. It's main characteristic is the introduction of a coder/decoder pair separate from the information source and destination - a view which we call the PDU paradigm. In terms of computer communications, the coder/decoder entities are known as protocol stacks which exchange highly structured protocol data units (PDU). All a receiving protocol stack has to do is to analyse each received PDU and, according to the data values found, react by either changing an internal state, by generating a new PDU or by delivering a 'decoded' message to the destination entity. The new paradigm, called messenger paradigm, replaces the exchange of data values by the exchange of instructions. Such groups of instructions, named messengers, are no longer analysed when received: they simply have to be executed. Part 1 of this work examines the messenger paradigm from a rather philosophical viewpoint by using the conceptual framework of semiotics, but also by relating the messenger paradigm with the virus mechanism found in biology and informatics. Part 2 applies the messenger paradigm to some protocols of computer communications and introduces the key elements of a first execution environment for messengers. It is shown how Stenning's sliding window protocol can be reformulated within the messenger context, thus leading to an implementation of this protocol which does no longer require preinstalled protocol entities. Unexpected theoretical problems become manifest when one tries to relate a messenger-based protocol realisation with its related ordinary PDU-based form. One of the conclusions of this work is that there may be protocols which can be expressed in terms of messengers but which have no equivalent representation under the PDU-paradigm. Part 3 finally investigates the consequences of applying the messenger paradigm to computer communications in general. Messengers offer in principle complete liberty for the structuring of computer communications. However, in order to be useful, some common structures (i.e. conventions) are necessary. The problems of setting up a meta-communication architecture are then discussed whereas it seems that new insights may come from extending the principle of computational reflection to a distributed environment, but also from existing theories of organisation, that is, cybernetics and sociology. More research is needed in order to better understand the implications of the messenger paradigm not only for computer communications, but also for a general theory of communication.

We focus on correlated queues where service and inter-arrival times are strongly correlated, and the input and output link speeds are the same. We present an analytical method to derive the LST (Laplace Stieltjes transform) of the (actual) waiting time distribution. To investigate the effect of correlation between service and inter-arrival times on the system performance, we consider a counterpart GI/G/1 queue where inter-arrival time and service time distributions are the same as in our correlated system, but they are independent. Some numerical examples are provided to show that such correlations have significant impact on the system performance.

The authors present performance measurements for data transfer services at the CASE (common application service elements), transport, and datalink layers of Motorola's implementation of the Manufacturing Automation Protocol (MAP) for a range of message sizes. They compare the performance results of using a stop-and-wait vs. a sliding window protocol, and find that the sliding window permits a 40% speedup. The observe that end-to-end latency exceeds transmission delay by a factor of 25 for 1000-byte messages, thereby making all network access, transmission, and propagation delays negligible when compared to protocol processing. They show that the throughput of CASE and transport is basically linear with message size whereas the throughput of datalink is not. They identify the bottlenecks which constrain total system throughput at each layer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A stepwise refinement heuristic to construct distributed systems is presented. The heuristic is based on a conditional refinement relation between system specifications, and a “Marking”. It is applied to construct four sliding window protocols that provide reliable data transfer over unreliable communication channels. The protocols use modulo- N sequence numbers. The first protocol is for channels that can only lose messages in transit. By refining this protocol, we obtain three protocols for channels that can lose, reorder, and duplicate messages in transit. The protocols herein are less restrictive and easier to implement than sliding window protocols previously studied in the protocol verification literature.