36676674
A note on the extended Blasius equation
Abstract In a recent paper, the Blasius equation was extended to a nonlinear equation like a f ‴ + f f ″ = 0 with the prime denoting differentiation with respect to the similarity variable η and a being a constant parameter. The current note will show that the solution of the extended Blasius equation can be obtained from the original Blasius equation solution with a variable transformation technique. The observed phenomena in numerical solutions of previous published work are theoretically analyzed. The equation is also discussed for an arbitrary real parameter or complex parameters. It is further shown that the extended Blasius equation is a special form of the similarity equation of momentum boundary layers over a flat plate with a temperature dependent property.
34460222
A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate
In the current work, the boundary layer flow of a slightly rarefied gas free stream over a moving flat plate is presented and solved numerically. The first-order slip boundary condition is adopted in the derivation. The dimensionless velocity and shear stress profiles are plotted and discussed. A theoretical derivation of the estimated solution domain is developed, which will give a very close estimation to the exact solution domain obtained numerically. The influences of velocity slip at the wall on the velocity and shear stress are also addressed.
16111193
Bounding Cache-Related Preemption Delay for Real-Time Systems
Cache memory is used in almost all computer systems today to bridge the ever increasing speed gap between the processor and main memory. However, its use in multitasking computer systems introduces additional preemption delay due to the reloading of memory blocks that are replaced during preemption. This cache-related preemption delay poses a serious problem in realtime computing systems where predictability is of utmost importance. We propose an enhanced technique for analyzing and thus bounding the cache-related preemption delay in fixed-priority preemptive scheduling focusing on instruction caching. The proposed technique improves upon previous techniques in two important ways. First, the technique takes into account the relationship between a preempted task and the set of tasks that execute during the preemption when calculating the cache-related preemption delay. Second, the technique considers the phasing of tasks to eliminate many infeasible task interactions. These two features are expressed as constraints of a linear programming problem whose solution gives a guaranteed upper bound on the cache-related preemption delay. This paper also compares the proposed technique with previous techniques using randomly generated task sets. The results show that the improvement on the worst-case response time prediction by the proposed technique over previous techniques ranges between 5 percent and 18 percent depending on the cache refill time when the task set utilization is 0.6. The results also show that as the cache refill time increases, the improvement increases, which indicates that accurate prediction of cache-related preemption delay by the proposed technique becomes increasingly important if the current trend of widening speed gap between the processor and main memory continues.
5311612
A genetic algorithm for job sequencing problems with distinct due dates and general early-tardy penalty weights
Abstract A job scheduling problem with distinct due dates in a single machine is considered. General penalty weights which are not necessarily proportional to the processing times are applied to jobs either early or tardy. An optimal timing algorithm is presented which decides the optimal starting time of each job in a given job sequence. Idle times are inserted between blocks of jobs such that the cost function of each newly created job block is minimized. Prominent near optimal sequences are generated via a genetic algorithm N best reproduction without duplicates, uniform order-based crossover and intra-block mutation operators are employed. The proposed genetic algorithm is proved to outperform existing heuristic methods. On average, 12–33% cost reduction effect is obtained by the evolution algorithm compared to the solution by an excellent heuristic procedure. The near optimality of the solutions by the GA is also illustrated by the comparison with an exact algorithm.
9253270
Query Optimization in Multidatabase Systems Considering Schema Conflicts
In a multidatabase system, the participating databases are autonomous. The schemas of these databases may be different in various ways, while the same information is represented. A global query issued against the global database needs to be translated to a proper form before it can be executed in a local database. Since data requested by a query (or a part of a query) is sometimes available in multiple sites, the site (database) that processes the query with the least cost is the desired query processing site. The authors study the effect of differences in schemas on the cost of query processing in a multidatabase environment. They first classify schema conflicts to different types. For each type of conflict, they show how much more or less complex a translated query can become in comparison with the originally user-issued global query. Based on this observation, they propose an analytical method that considers the conflicts between local databases and finds the database(s) that renders the least execution cost in processing a global query. This research introduces a new level of query optimization (termed the schema-level optimization) in multidatabase environments. The results provide a new dimension of enhancement for the capability of a query optimizer in multidatabase systems.
8596907
Multiple multicast tree allocation in IP network
The multicasting is defined as the distribution of the same information stream from one to many nodes concurrently. There has been an intensive research effort to design protocols and construct multicast routing graphs for a single multicast group. In this paper, the multiple multicast tree allocation problem is discussed and algorithms are proposed to solve the congestion problem in the IP network. As the congestion measure the minimum residual capacity is considered. Two phase algorithm MMTA is investigated for multiple multicast tree allocation both for identical and different bandwidth requirement by the multicast groups. The central and distributed implementation of the multiple multicast tree is discussed for the deployment in the real IP network. The performance of the proposed MMTA is compared with other procedures. Computational results show that the two-phase MMTA outperforms other procedures. Approximately 3-7% improvement in the residual capacity is obtained by the MMTA. The solution gap from the upper bound by the well-known branch and bound is within 2-11% depending on the problem size.
7460330
Enhanced analysis of cache-related preemption delay in fixed-priority preemptive scheduling
We propose an enhanced technique for analyzing, and thus bounding cache related preemption delay in fixed priority preemptive scheduling focusing on instruction caching. The proposed technique improves upon previous techniques in two important ways. First, the technique takes into account the relationship between a preempted task and the set of tasks that execute during the preemption when calculating the cache related preemption delay. Second, the technique considers phasing of tasks to eliminate many infeasible task interactions. These two features are expressed as constraints of a linear programming problem whose solution gives a guaranteed upper bound on the cache related preemption delay. The paper also compares the proposed technique with previous techniques. The results show that the proposed technique gives up to 60% tighter prediction of the worst case response time than the previous techniques.