scholarly journals Stability of Switched Server Systems with Constraints on Service-Time and Capacity of Buffers

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Li Wang ◽  
Zhonghe He ◽  
Chi Zhang
Keyword(s):  
Periodic Orbit ◽  
Service Time ◽  
Buffer Capacity ◽  
Time Factors ◽  
Upper Bounds ◽  
Finite Buffer ◽  
Lower And Upper Bounds ◽  
Upper Limit ◽  
Server Systems ◽  
The Given

The execution of emptying policy ensures the convergence of any solution to the system to a unique periodic orbit, which does not impose constraints on service-time and capacity of buffers. Motivated by these problems, in this paper, the service-time-limited policy is first proposed based on the information resulted from the periodic orbit under emptying policy, which imposes lower and upper bounds on emptying time for the queue in each buffer, by introducing lower-limit and upper-limit service-time factors. Furthermore, the execution of service-time-limited policy in the case of finite buffer capacity is considered. Moreover, the notion of feasibility of states under service-time-limited policy is introduced and then the checking condition for feasibility of states is given; that is, the solution does not exceed the buffer capacity within the first cycle of the server. At last, a sufficient condition for determining upper-limit service-time factors ensuring that the given state is feasible is given.

Statistical properties of simple types

2000 ◽  
Vol 10 (5) ◽  
pp. 575-594 ◽  
Author(s):  
M. MOCZURAD ◽  
J. TYSZKIEWICZ ◽  
M. ZAIONC
Keyword(s):  
Finite Number ◽  
Lambda Calculus ◽  
Upper Bounds ◽  
Statistical Properties ◽  
Propositional Variable ◽  
Lower And Upper Bounds ◽  
Type Formula ◽  
Ground Types ◽  
Asymptotic Probability ◽  
The Given

We consider types and typed lambda calculus over a finite number of ground types. We are going to investigate the size of the fraction of inhabited types of the given length n against the number of all types of length n. The plan of this paper is to find the limit of that fraction when n → ∞. The answer to this question is equivalent to finding the ‘density’ of inhabited types in the set of all types, or the so-called asymptotic probability of finding an inhabited type in the set of all types. Under the Curry–Howard isomorphism this means finding the density or asymptotic probability of provable intuitionistic propositional formulas in the set of all formulas. For types with one ground type (formulas with one propositional variable), we prove that the limit exists and is equal to 1/2 + √5/10, which is approximately 72.36%. This means that a long random type (formula) has this probability of being inhabited (tautology). We also prove that for every finite number k of ground-type variables, the density of inhabited types is always positive and lies between (4k + 1)/(2k + 1)2 and (3k + 1)/(k + 1)2. Therefore we can easily see that the density is decreasing to 0 with k going to infinity. From the lower and upper bounds presented we can deduce that at least 1/3 of classical tautologies are intuitionistic.

Wrench Accuracy for Parallel Manipulators and Interval Dependency

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Interval Arithmetic ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Upper Bounds ◽  
Solution Set ◽  
Lower And Upper Bounds ◽  
Solution Sets ◽  
The Given

In this paper, the wrench accuracy for parallel manipulators is examined under variations in parameters and data. The solution sets of actuator forces/torques are investigated utilizing interval arithmetic (IA). Implementation issues of interval arithmetic to analyze the performance of manipulators are addressed, including the consideration of dependencies in parameters and the design of input vectors to generate the required wrench. Specifically, the effect of the dependency within and among the entries of the Jacobian matrix is studied, and methodologies for reducing and/or eliminating the overestimation of solution set are presented. In addition, the subset of solution set that produces platform wrenches within the required lower and upper bounds is modeled. Furthermore, the formulation of solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.

scholarly journals The inverse maximum flow problem under Lk norms

2012 ◽  
Vol 28 (1) ◽  
pp. 59-66
Author(s):  
ADRIAN DEACONU ◽  
◽  
ELEONOR CIUREA ◽  
Keyword(s):  
Polynomial Time ◽  
Flow Problem ◽  
Maximum Flow ◽  
Upper Bounds ◽  
Initial Vector ◽  
Lower And Upper Bounds ◽  
Maximum Flow Problem ◽  
The Given

The problem consists in modifying the lower and upper bounds of a given feasible flow f in a network G so that the given flow becomes a maximum flow in G and the distance between the initial vector of bounds and the modified one measured using Lk norm (k ∈ N∗) is minimum. A fast apriori fesibility test is presented. An algorithm for solving this problem is deduced. Strongly and weakly polynomial time implementations of this algorithm are presented. Some particular cases of the problem are discussed.

scholarly journals Bounds for the variance of the busy period of the M/G/∞ queue

1984 ◽  
Vol 16 (4) ◽  
pp. 929-932 ◽  
Author(s):  
M. F. Ramalhoto
Keyword(s):  
Distribution Function ◽  
Lower Bounds ◽  
Service Time ◽  
Time Distribution ◽  
Busy Period ◽  
Random Variable ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Service Time Distribution ◽  
Lower And Upper Bounds

Some bounds for the variance of the busy period of an M/G/∞ queue are calculated as functions of parameters of the service-time distribution function. For any type of service-time distribution function, upper and lower bounds are evaluated in terms of the intensity of traffic and the coefficient of variation of the service time. Other lower and upper bounds are derived when the service time is a NBUE, DFR or IMRL random variable. The variance of the busy period is also related to the variance of the number of busy periods that are initiated in (0, t] by renewal arguments.

scholarly journals Bounds for the variance of the busy period of the M/G/∞ queue

1984 ◽  
Vol 16 (04) ◽  
pp. 929-932
Author(s):  
M. F. Ramalhoto
Keyword(s):  
Distribution Function ◽  
Lower Bounds ◽  
Service Time ◽  
Time Distribution ◽  
Busy Period ◽  
Random Variable ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Service Time Distribution ◽  
Lower And Upper Bounds

Some bounds for the variance of the busy period of an M/G/∞ queue are calculated as functions of parameters of the service-time distribution function. For any type of service-time distribution function, upper and lower bounds are evaluated in terms of the intensity of traffic and the coefficient of variation of the service time. Other lower and upper bounds are derived when the service time is a NBUE, DFR or IMRL random variable. The variance of the busy period is also related to the variance of the number of busy periods that are initiated in (0, t] by renewal arguments.

Dimensioning On-Demand Vehicle Sharing Systems

2021 ◽  
Author(s):  
Saif Benjaafar ◽  
Shining Wu ◽  
Hanlin Liu ◽  
Einar Bjarki Gunnarsson
Keyword(s):  
Closed Form ◽  
Buffer Capacity ◽  
Correction Term ◽  
Queueing Network ◽  
Service Level ◽  
Upper Bounds ◽  
Optimal Number ◽  
Lower And Upper Bounds ◽  
Service Completion ◽  
Wide Range

We consider the problem of optimal fleet sizing in a vehicle sharing system. Vehicles are available for short-term rental and are accessible from multiple locations. A vehicle rented at one location can be returned to any other location. The size of the fleet must account not only for the nominal load and for the randomness in demand and rental duration but also for the randomness in the number of vehicles that are available at each location because of vehicle roaming (vehicles not returning to the same location from which they were picked up). We model the dynamics of the system using a closed queueing network and obtain explicit and closed form lower and upper bounds on the optimal number of vehicles (the minimum number of vehicles needed to meet a target service level). Specifically, we show that starting with any pair of lower and upper bounds, we can always obtain another pair of lower and upper bounds with gaps between the lower and upper bounds that are independent of demand and bounded by a function that depends only on the prescribed service level. We show that the generated bounds are asymptotically exact under several regimes. We use features of the bounds to construct a simple and closed form approximation that we show to be always within the generated lower and upper bounds and is exact under the asymptotic regimes considered. Extensive numerical experiments show that the approximate and exact values are nearly indistinguishable for a wide range of parameter values. The approximation is highly interpretable with buffer capacity expressed in terms of three explicit terms that can be interpreted as follows: (1) standard buffer capacity that is protection against randomness in demand and rental times, (2) buffer capacity that is protection against vehicle roaming, and (3) a correction term. Our analysis reveals important differences between the optimal sizing of standard queueing systems (where servers always return to the same queue upon service completion) and that of systems where servers, upon service completion, randomly join any one of the queues in the system. We show that the additional capacity needed to buffer against vehicle roaming can be substantial even in systems with vanishingly small demand. This paper was accepted by Baris Ata, stochastic models and simulation.

scholarly journals Lower and Upper Bounds for the Discrete Bi-Directional Preemptive Conversion Problem with a Constant Price Interval

Algorithms ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 42
Author(s):  
Michael Schwarz
Keyword(s):  
Competitive Analysis ◽  
Upper Bound ◽  
Competitive Ratio ◽  
Upper Bounds ◽  
Investment Horizon ◽  
Lower And Upper Bounds ◽  
Single Period ◽  
Price Trends ◽  
The Given ◽  
Period Model

In the conversion problem, wealth has to be distributed between two assets with the objective to maximize the wealth at the end of the investment horizon. The bi-directional preemptive conversion problem with a constant price interval is the only problem, of the four main variants of the conversion problem, that has not yet been optimally solved by competitive analysis. Assuming a given number of monotonous price trends called runs, lower and upper bounds for the competitive ratio are given. In this work, the assumption of a given number of runs is rejected and lower and upper bounds for the bi-directional preemptive conversion problem with a constant price interval are given. Furthermore, an algorithm based on error balancing is given which at minimum achieves the given upper bound. It can also be shown that this algorithm is optimal for the single-period model.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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