M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem

We propose in this article a M/G/c/c state dependent queuing model for road traffic flow. The model is based on finite capacity queuing theory which captures the stationary density-flow relationships. It is also inspired from the deterministic Godunov scheme for the road traffic simulation. We first present a reformulation of the existing linear case of M/G/c/c state dependent model, in order to use flow rather than speed variables. We then extend this model in order to consider upstream traffic demand and downstream traffic supply. After that, we propose the model for two road sections in tandem where both sections influence each other. In order to deal with this mutual dependence, we solve an implicit system given by an algebraic equation. Finally, we derive some performance measures (throughput and expected travel time). A comparison with results predicted by the M/G/c/c state dependent queuing networks shows that the model we propose here captures really the dynamics of the road traffic.     

The Diameter and Average Distance of Supertoroidal Networks

The subject of this paper is a family of network topologies which are intended to be practical enough to be implemented in a parallel computer using contemporary technology. These network topologies offer an alternative to the three-dimensional mesh or toroid and are most likely to be useful for a network with between 512 and 16,384 nodes. The topologies, which are called supertoroids, are Cayley graphs of groups. The groups are semidirect products of two cyclic groups, one of order ck and the other of order c²l. The resulting Cayley graph has c³kl vertices and is of degree 4. The main results of this paper are two theorems. The first states that the diameter of the supertoroidal network with c³kl nodes is [cl/2] + [ck/2] if c ≥ 8. The second states that the average distance is asymptotically (in c) equal to ([cl/2] + [ck/2])/2. Because of these facts, the supertoroidal network has latency which is lower than the latency of a three-dimensional toroid of the same size. Although the proofs of these theorems are a tour-de-force of arithmetic in the underlying group, they are based upon exploitation of parallelism of paths in a Cayley graph.     

A Compiler-Directed Approach to Network Latency Reduction for Distributed Shared Memory Multiprocessors

In distributed shared memory multiprocessor systems, parallel tasks communicate through sharing memory data. As the system size increases, such communication cost becomes the main factor that limits the overall parallelism and performance. In this paper, we propose a new solution to the problem through judiciously managing the relevant resource, namely, the shared data and the interconnection network (IN) through which the sharing is carried out. In this approach, communication cost is minimized by means of data migration/allocation which is based on analyzing general layered task graphs, sharing behavior of parallel tasks, and network topology. Our method is not applicable for read only variables. Further, for the time being, the usefulness of the method is limited to multiprocessors where no cache coherence mechanism is implemented. Four typical interconnection topologies for multiprocessors are considered, namely, shared-bus, hierarchical-bus, 2-D mesh, and fat-tree structures. Efficient data allocation algorithms for each of the four network topologies are developed that make decision on data allocation/migration at the compile time. The complexity of one algorithm isO(np) for shared-bus andO(n²p) for the remaining three in a system withnprocessors executing ap-layer task graph for one shared variable. We have also given an algorithm to determine optimal allocation/migration scheme for multiple shared variables. However, the cost of the algorithm become prohibitive when the number of shared variables is high. Therefore, a heuristic of low complexity is suggested. The heuristic is optimal for some topologies.     

Approximate analysis of M/G/c/c state-dependent queueing networks

Congestion is ever present in most practical situations. We describe a methodology for approximate analysis of open state-dependent M/G/c/c queueing networks in which the service rate is subject to congestion, that is, it is a function of the number of customers in the system. Important performance measurements are easily computed with high accuracy, such as the blocking probability, throughput, expected number of customers in the system (known also as work-in-process), and expected waiting time. The methodology forms a basic building block useful in many practical applications and contexts. Computational results demonstrate that the methodology provides accurate results in many topological configurations as well as in the analysis of network evacuation problems in high-rise buildings.     

Analysis of GI/M/s/c queues using uniformisation

We combine uniformisation, a powerful numerical technique for the analysis of continuous time Markov chains, with the Markov chain embedding technique to analyze GI/M/s/c queues. The main steps of the proposed approach are the computation of

• (1)the mixed-Poisson probabilities associated to the number of arrival epochs in the uniformising Poisson process between consecutive customer arrivals to the system; and
• (2)the conditional embedded uniformised transition probabilities of the number of customers in the queueing system immediately before customer arrivals to the system.

To show the performance of the approach, we analyze queues with Pareto interarrival times using a stable recursion for the associated mixed-Poisson probabilities whose computation time is linear in the number of computed coefficients. The results for queues with Pareto interarrival times are compared with those obtained for queues with other interarrival time distributions, including exponential, Erlang, uniform and deterministic interarrival times. The obtained results show that much higher loss probabilities and mean waiting times in queue may be obtained for queues with Pareto interarrival times than for queues with the other mentioned interarrival time distributions, specially for small traffic intensities.     

C-correction of optical satellite data over alpine vegetation areas: A comparison of sampling strategies for determining the empirical c-parameter

Semi-empirical topographic normalization methods (e.g., C-correction) have been widely used to correct illumination differences in optical satellite data. The objective of this study was to examine the precision and accuracy of the C-correction's empirical parameter, c, as a function of the sample from which it was derived. Three sampling methods were compared: a random sample, a sample stratified on north and south aspects, and a sample stratified by cosine of the solar incidence angle, i. In the latter, power allocation was used to determine the quantity of observations for each stratum. Four overlapping satellite images were used (two Landsat 5 TM and two SPOT 5 HRG) with different acquisition dates and large solar zenith angles over an alpine region in Sweden. The sample stratified by cosine of i produced c with the highest precision from repeated trials and had coefficients of determination (R²) twice as high as those from the other sampling methods. Use of power allocation in the cosine of i stratified sample enabled better representation of spectral variability; this was particularly important for the NIR band where the outcome of c differed according to sampling method. Evaluations using t-tests and classification accuracy showed that c derived from the cosine of i stratified sample correctly normalized a larger percentage of the evaluation data. The distribution of cosine of i in the study area, the spectral variability and vegetation types exert influences to consider when sampling to derive c. Although sampling was restricted to alpine vegetation only, some vegetation classes may have benefitted from separate c-parameter calculation. In general, dry alpine heath and alpine grass heath had relatively higher c-parameters, mesic alpine heath was slightly lower, and alpine willow and alpine meadow had lower c-parameters for the near-infrared band. The cosine of i stratified sampling method using power allocation may be useful for calculation of c for vegetation conditions other than those presented here, as well as for other empirical parameters (e.g., the Minnaert constant, k).     

Combining a maintenance center M/M/c/m queue into the economic production quantity model with stochastic machine breakdowns and repair

This article considers a production system in which “m” identical machines produce nonidentical products at production rates. Products made by each machine are on the other hand consumed at a specific demand rate. Machines may be affected by unwanted breakdowns. Machines break down according to a Poisson distribution with equal rates and the failed machines are sent to maintenance center for repair which is consisted of “c” servers or servicemen. However, Number of machines is greater than number of servicemen (m > c). Hence, if the number of failed machines is greater than that of servicemen, the machines have to be put in a queue. Machines are put in one queue with the order of queue being FCFS. The queue has a typical M/M/c/m system. If machines are broken down during production, shortage will occur. This problem has been considered to obtain a single production cycle for the machines and an optimum number of the servers such that costs are minimized. For this purpose, distribution of waiting time for machines in repair center is calculated and a cost function is formed. Steepest descent and direct search methods are applied in this work to obtain optimal production cycle and maintenance servers, respectively. The proposed methods are studied using a comprehensive example.     

Combining a maintenance center M/M/c/m queue into the economic production quantity model with stochastic machine breakdowns and repair

This article considers a production system in which “m” identical machines produce nonidentical products at production rates. Products made by each machine are on the other hand consumed at a specific demand rate. Machines may be affected by unwanted breakdowns. Machines break down according to a Poisson distribution with equal rates and the failed machines are sent to maintenance center for repair which is consisted of “c” servers or servicemen. However, Number of machines is greater than number of servicemen (m > c). Hence, if the number of failed machines is greater than that of servicemen, the machines have to be put in a queue. Machines are put in one queue with the order of queue being FCFS. The queue has a typical M/M/c/m system. If machines are broken down during production, shortage will occur. This problem has been considered to obtain a single production cycle for the machines and an optimum number of the servers such that costs are minimized. For this purpose, distribution of waiting time for machines in repair center is calculated and a cost function is formed. Steepest descent and direct search methods are applied in this work to obtain optimal production cycle and maintenance servers, respectively. The proposed methods are studied using a comprehensive example.     

Maximal c consensus meets

Given a set S of subsets of a reference set X, we define the problem of finding c subsets of X that maximize the size of the intersection among the included subsets. Maximizing the size of the intersection means that they are subsets of the sets in S and they are as large as possible.We can understand the result of this problem as c consensus sets of S, or c consensus representatives of S. From the perspective of lattice theory, each representative will be a meet of some sets in S.In this paper we define formally this problem, and present heuristic algorithms to solve it. We also discuss the relationship with other established problems in the literature.     

An optimal parallel algorithm for c-vertex-ranking of trees

For a positive integer c, a c-vertex-ranking of a graph G=(V,E) is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels >i leaves connected components, each having at most c vertices with label i. The c-vertex-ranking problem is to find a c-vertex-ranking of a given graph using the minimum number of ranks. In this paper we give an optimal parallel algorithm for solving the c-vertex-ranking problem on trees in O(log₂n) time using linear number of operations on the EREW PRAM model.     

Effects of different solvents on the conformations of apoptotic cytochrome c: Structural insights from molecular dynamics simulation

Cytochrome c (cyt-c) upon binding with cardiolipin acquires peroxidase activity and is strictly connected to the pathogenesis of many human diseases including neurodegenerative and cardiovascular diseases. Interaction of cyt-c with cardiolipin mimics partial unfolding/conformational changes of cyt-c in different solvent environments. Dynamic pictures of these conformational changes of cyt-c are crucial in understanding their physiological roles in mitochondrial functions. Therefore, atomistic molecular dynamics (MD) simulations have been carried out to investigate the effect of different solvents (water, urea/water, MeOH and DMSO) on the structure and conformations of apoptotic cyt-c (Fe³⁺). Our study demonstrates that the structural changes in the protein are solvent dependent. The structural differences are observed majorly on the β-sheets and α-helical conformations and the degree of their perturbation are specific to the solvent. Although a complete loss of β-sheets (0%) is observed in MeOH and DMSO, by contrast, well preserved β-sheets (3.84%) are observed in water and urea/water. A significant decrease in the α-helical contents is observed in MeOH (41.34%) and water (42.46%), a negligible alteration in DMSO (44.25%) and well preserved α-helical (45.19%) contents in urea/water. The distances between the residues critical for electron transfer are decreased considerably for DMSO. Further, the reduction in residue flexibility and the conformational space indicate that the collective motions of cyt-c are reduced when compared to other cosolvents. Essential dynamics analysis implies that the overall motions of cyt-c in water, MeOH and urea/water are involved in three to four eigenvectors and in first eigenvector in DMSO. Overall, we believe that MD simulations of cyt-c in different solvents can provide a detailed microscopic understanding of the physiological roles, electron transport and peroxidase function in the early events of apoptosis which are hard to probe experiments.     

Approximation and complexity of the optimization and existence problems for maximin share,proportional share,and minimax share allocation of indivisible goods

This paper is concerned with various types of allocation problems in fair division of indivisible goods, aiming at maximin share, proportional share, and minimax share allocations. However, such allocations do not always exist, not even in very simple settings with two or three agents. A natural question is to ask, given a problem instance, what is the largest value c for which there is an allocation such that every agent has utility of at least c times her fair share. We first prove that the decision problem of checking if there exists a minimax share allocation for a given problem instance is \(\mathrm {NP}\)-hard when the agents’ utility functions are additive. We then show that, for each of the three fairness notions, one can approximate c by a polynomial-time approximation scheme, assuming that the number of agents is fixed. Next, we investigate the restricted cases when utility functions have values in \(\{0,1\}\) only or are defined based on scoring vectors (Borda and lexicographic vectors), and we obtain several tractability results for these cases. Interestingly, we show that maximin share allocations can always be found efficiently with Borda utilities, which cannot be guaranteed for general additive utilities. In the nonadditive setting, we show that there exists a problem instance for which there is no c-maximin share allocation, for any constant c. We explore a class of symmetric submodular utilities for which there exists a tight \(\frac{1}{2}\)-maximin share allocation, and show how it can be approximated to within a factor of \(\nicefrac {1}{4}\).     

Surface Reconstruction between Simple Polygons via Angle Criteria

We consider the problem of connecting two simple polygons P and Q in parallel planes by a polyhedral surface. The goal is to find an optimality criterion which naturally satisfies the following conditions: (i) if P and Q are convex, then the optimal surface is the convex hull of P and Q (without facets P and Q), and (ii) if P can be obtained from Q by scaling with a center c, then the optimal surface is the portion of the cone defined by P and apex c between the two planes. We provide a criterion (based on the sequences of angles of the edges of P and Q), which satisfies these conditions, and for which the optimal surface can be efficiently computed. Moreover, we supply a condition, so-called angle consistency, which proved very helpful in preventing self intersections (for our and other criteria). The methods have been implemented and gave improved results in a number of examples.     

Properties and performance modelling of finite buffer M/G/1/K networks

Finite buffer, single-server queueing systems and networks are difficult to analyze since the length of time a customer spends in the system does not follow the Markovian property. A two-moment approximation schema is developed for the probability distribution of M/G/1/K systems and extended to the analysis of M/G/1/K   queueing networks. The general purpose of this paper is to develop a flexible and practical transform-free approach for computing the probability distribution and performance measures of the system as well as identify the underlying properties of these systems. It is shown that for most performance measures, a sigmoid or S-shaped curve with an inflection point at ρ=1$\rho =1$ appears as K→∞$K\to \infty$. This has direct implications for the analysis and optimization of such systems. The performance modelling of the M/G/1/K queueing networks of general topologies along with extensive numerical results accompany the paper along with the linear concave performance measures for these systems.     

Task assignment in Cayley interconnection topologies

Based on the Cayley graph framework for the generation and evaluation of multiprocessor interconnection topologies, an application dependent task mapping problem is addressed. We start with interconnection topologies considered attractive from a graph theoretical point of view. Given such a topology together with an application dependent task communication profile, the problem addressed in this paper is to find an optimal task-to-processor assignment. Such a mapping yields for the given interconnection topology and the given profile a minimal expected communication path length and therefore a minimal number of data transfer steps between the physical processing elements of a multiprocessor machine. At first, the Cayley graph approach is briefly outlined. We demonstrate the potential of Cayley graphs for a systematic generation framework aiming at node-symmetric interconnection topologies for a given number of processing elements each equipped with a constant number of communication channels. Cayley graphs found most attractive within a large set of generated graphs are compared to prominent interconnection topologies like, for example, hypercubes. Later on, it is shown that the problem of the optimal task-to-processor assignment, being a special case of the well-known quadratic assignment problem, is still NP-hard. Consequently, any practically relevant mapping algorithm can be expected to produce at best near-optimal solutions for reasonable problem sizes beyond approximately 10 nodes. We present two fundamentally different mapping approaches, namely a straightforward greedy mapping and a more sophisticated algorithm using simulated annealing techniques as known from artificial intelligence applications. For both approaches, we elaborate on their relative performance as well as, where feasible, on the question of suboptimality.     

Joint object placement and node dimensioning for Internet content distribution

This paper studies a resource allocation problem in a graph, concerning the joint optimization of capacity allocation decisions and object placement decisions, given a single capacity constraint. This problem has applications in Internet content distribution and other domains. The solution to the problem comes through a multi-commodity generalization of the single commodity k-median problem. A two-step algorithm is developed that is capable of solving the multi-commodity case optimally in polynomial time for the case of tree graphs, and approximately (within a constant factor of the optimal) in polynomial time for the case of general graphs.     

Approximations for the waiting time distribution of the M/G/c queue

For the M/G/c queue we present an approximate analysis of the waiting time distribution. The result is given in the form of the defective renewal equation. This integral equation can be numerically solved by a simple recursion procedure. Also, asymptotic results for the waiting times are presented. Numerical results indicate that the approximations are sufficiently accurate for practical purposes.     

A neural networks algorithm for data path synthesis

This paper presents a deterministic parallel algorithm to solve the data path allocation problem in high-level synthesis. The algorithm is driven by a motion equation that determines the neurons firing conditions based on the modified Hopfield neural network model of computation. The method formulates the allocation problem using the clique partitioning problem, an NP-complete problem, and handles multicycle functional units as well as structural pipelining. The algorithm has a running time complexity of O(1) for a circuit with n operations and c shared resources. A sequential simulator was implemented on a Linux Pentium PC under X-Windows. Several benchmark examples have been implemented and favorable design comparisons to other synthesis systems are reported.     

Distributed Latency-Energy Minimization and interference avoidance in TDMA Wireless Sensor Networks

This paper presents Latency-Energy Minimization Medium Access (LEMMA), a new TDMA-based MAC protocol for Wireless Sensor Networks (WSNs), specially suited to extend the lifetime of networks supporting alarm-driven, delay-sensitive applications characterized by convergecast traffic patterns and sporadic traffic generation. Its cascading time-slot assignment scheme conciliates low end-to-end latency with a low duty-cycle, while supporting multi-sink WSN topologies. Unlike most of the current solutions, LEMMA’s time-slot allocation protocol makes decisions based on the interference actually experienced by the nodes, instead of following the simple but potentially ineffective n-hop approach. Simulation results are presented to demonstrate the ineffectiveness of the n-hop time-slot allocation in comparison with LEMMA, as well as to evaluate the performance of LEMMA against L-MAC, T-MAC and Low Power Listening. The results show that under the target scenario conditions, LEMMA presents lower interference between assigned time-slots and lower end-to-end latency, while matching its best contender in terms of energy-efficiency.