In this note we present an implementation of the fast marching algorithm for solving Eikonal equations that reduces the original run-time from O(N log N) to linear. This lower run-time cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm. This improvement is achieved introducing the straight forward untidy priority queue, obtained via a quantization of the priorities in the marching computation. We present the underlying framework, estimations on the error, and examples showing the usefulness of the proposed approach. Key words: Fast marching, Hamilton-Jacobi and Eikonal equations, distance functions, bucket sort, untidy priority queue.

We report on the design objectives and initial design of a new discrete-event network simulator for the research community. Creating Yet Another Network Simulator (yans,

Abstract. Priority queues are widely employed in numerous applications such discrete event simulations (DESs). The priority queue structure plays an integral role of managing the pending event set of a DES. The priority queue contains events where the minimum timestamp event has the highest priority and the maximum timestamp event has the lowest priority. A Calendar Queue (CQ) is a useful structure often employed in DESs. Its popularity is due to its expected O(1) access time for many simulation scenarios, provided the CQ resizes appropriately frequent to ensure that events are evenly distributed in the CQ structure. The resize operation is triggered whenever the number of events fluctuates significantly or when a skewed event distribution is detected. A resize operation is costly as it copies events from the old CQ structure to a newly-created one. Other CQ variants such as the Dynamic CQ and SNOOPy exhibit somewhat futile attempts to improve the heuristics involve in triggering the resize operation. This article introduces a novel priority queue implementation known as the Dynamic Splay Tree (DSplay) structure which does not require the resize operation to obtain near O(1) performance. The DSplay is also empirically shown to be on the average at least 100 % faster than all the current priority queues. 1.

Pending event set (PES) structures are used in discrete event simulations to manage events according to their timestamps. A PES structure enqueues timestamped events according to priority, where the earlier events are enqueued at the head of the queue and later events at the end of the queue. The implementation of the PES structure will greatly affect its efficiency and hence the performance of discrete event simulations. This thesis looks into the performance of priority queue structures used to implement the PES. In particular, the calendar queue (CQ), which is widely accepted as having superior performance, and its variant improvements, are analyzed in detail. The analysis shows that while the CQ performs well under most situations, its performance suffers greatly when the inter-arrival pattern of events, is highly skewed and when there are large size fluctuations. Also, improvements to the CQ, such as the Dynamic Calendar Queue (DCQ) and the SNOOPy CQ continue to be plagued by costly resize operations as the queue size increases. In addition, when the queue size becomes too large, statistical variation in inter-arrival patterns becomes too generalized, making the selection of optimum operating parameters difficult. Other priority queue structures, such as the Lazy Queue and Dynamic Lazy Calendar Queue (DLCQ) make use of a `lazy' queuing algorithm to limit the primary queue size by adding another data structure to store events that are too far away for enqueuing in the primary structure. In this thesis, we propose a new lazy extension to the CQ structure, henceforth referred to as the Far future Event Leaf Tree (FELT) ii extension. FELT is based on a novel size-based algorithm that performs much better than previous lazy algorithms by effectively limiting the calend...

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Abstract – There are many research efforts for improving bandwidth management in wireless communication systems based mainly on DCA (Dynamic Channel Allocation) Schemes designed and evaluated through various Simulation models which, however, use a common simulation model architecture coming from queuing theory. Although much attention has been paid to Channel Allocation Mechanisms there are few only efforts related to the corresponding simulation models. These models consist of various critical components including network services models and the simulation model architecture organizing network events scheduling, network events handling and network performance evaluation. One of the most critical components is the event scheduling mechanism, which reflects network events as they happen in a real network and which has not been investigated in depth regarding its performance. The state of the art event scheduling mechanism called Calendar Queue (CQ) schedules events for later execution based on the corresponding time stamps of each generated event. The major drawback of this approach is that the generated events are executed only sequentially due to progressive time stamps. On the other hand, events in a real wireless network happen concurrently and so the state of the art mechanism can not reflect such conditions. The goal of this paper is to propose an alternative novel real time scheduling mechanism based on a synthesis of multitasking theory and queuing theory techniques, which could be involved in generating and investigating a new generation of event

Abstract- The physical activities of a real wireless network are represented by events which are the main components of a discrete event simulation (DES) system and are produced by its event generator during simulation time. Each network service (e.g. voice, data and video) constitutes an event for a particular mobile user. A critical component within the simulation system, called scheduler, runs by selecting the next earliest event, executing it till completion, and returning to execute the next event. Calendar queue is the state of the art implementation of the scheduler among the most popular networking simulation tools such as ns-2. However, Calendar queue time-stamping mechanism presents drawbacks in the case of complex dynamical systems, like wireless networks, where probability of events concurrency is large. In such a case sequential time-stamping of calendar queue scheduling does not reflect real network events occurrence and generation. It should be remarked that there are very few reports if any in the literature concerning research on events scheduling mechanisms in such real time systems. On the other hand, multi-threading technology offers advanced capabilities for modelling concurrent events. The main goal of this paper is to illustrate that multithreading architectures provide the means for designing efficient schedulers in the simulation of wireless networks resource allocation but, also, several critical issues such as deadlocks, synchronization and scheduling must be effectively faced. In this paper, a stable simulation model is presented based on a novel layered thread