A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

Nonlinear programming solutions for controlling the vibration pattern of stretched strings

The problem of controlling the vibration pattern of a driven string is considered. The basic question dealt with here is to find the control forces which reduce the energy of vibration of a driven string over a prescribed portion of its length while maintaining the energy outside that length above a desired value. The criterion of keeping the response outside the region of energy reduction as close to the original response as possible is introduced as an additional constraint. The slack unconstrained minimization technique (SLUMT) has been successfully applied to solve the above problem. The effect of varying the phase of the control forces (which results in a six-variable control problem) is then studied. The nonlinear programming techniques which have been effectively used to handle problems involving many variables and constraints therefore offer a powerful tool for the solution of vibration control problems.

Ordered Ports – a Language Concept for High-level Distributed Programming

A new language concept for high-level distributed programming is proposed. Programs are organised as a collection of concurrently executing processes. Some of these processes, referred to as liaison processes, have a monitor-like structure and contain ports which may be invoked by other processes for the purposes of synchronisation and communication. Synchronisation is achieved by conditional activation of ports and also through port control constructs which may directly specify the execution ordering of ports. These constructs implement a path-expression-like mechanism for synchronisation and are also equipped with options to provide conditional, non-deterministic and priority ordering of ports. The usefulness and expressive power of the proposed concepts are illustrated through solutions of several representative programming problems. Some implementation issues are also considered.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

A functional style of programming with CSP-like communication mechanisms

This paper introduces CSP-like communication mechanisms into Backus’ Functional Programming (FP) systems extended by nondeterministic constructs. Several new functionals are used to describe nondeterminism and communication in programs. The functionals union and restriction are introduced into FP systems to develop a simple algebra of programs with nondeterminism. The behaviour of other functionals proposed in this paper are characterized by the properties of union and restriction. The axiomatic semantics of communication constructs are presented. Examples show that it is possible to reason about a communicating program by first transforming it into a non-communicating program by using the axioms of communication, and then reasoning about the resulting non-communicating version of the program. It is also shown that communicating programs can be developed from non-communicating programs given as specifications by using a transformational approach.

An efficient algorithm for linear programming

A simple but efficient algorithm is presented for linear programming. The algorithm computes the projection matrix exactly once throughout the computation unlike that of Karmarkar’s algorithm where in the projection matrix is computed at each and every iteration. The algorithm is best suitable to be implemented on a parallel architecture. Complexity of the algorithm is being studied.

Missile battery placement for air defense: A dynamic programming approach

A procedure to evaluate surface-to-air missile battery placement patterns for air defense is presented. A measure of defense effectiveness is defined as a function of kill probability of the defense missiles and the nature of the surrounding terrain features. The concept of cumulative danger index is used to select the best path for a penetrating hostile aircraft for any given pattern of placement. The aircraft is assumed to be intelligent and well-informed. The path is generated using a dynamic programming methodology. The software package so developed can be used off-line to choose the best among a number of possible battery placement patterns.

Positional Consensus of Multi-Agent Systems Using Linear Programming Based Decentralized Control with Rectilinear Decision Domain

In this paper we develop a Linear Programming (LP) based decentralized algorithm for a group of multiple autonomous agents to achieve positional consensus. Each agent is capable of exchanging information about its position and orientation with other agents within their sensing region. The method is computationally feasible and easy to implement. Analytical results are presented. The effectiveness of the approach is illustrated with simulation results.

Solving linear programming problems exactly

A linear programming problem in an inequality form having a bounded solution is solved error-free using an algorithm that sorts the inequalities, removes the redundant ones, and uses the p-adic arithmetic. (C) Elsevier Science Inc., 1997

Machine-tool selection and operation allocation in FMS: solving a fuzzy goal-programming model using a genetic algorithm

The decision-making process for machine-tool selection and operation allocation in a flexible manufacturing system (FMS) usually involves multiple conflicting objectives. Thus, a fuzzy goal-programming model can be effectively applied to this decision problem. The paper addresses application of a fuzzy goal-programming concept to model the problem of machine-tool selection and operation allocation with explicit considerations given to objectives of minimizing the total cost of machining operation, material handling and set-up. The constraints pertaining to the capacity of machines, tool magazine and tool life are included in the model. A genetic algorithm (GA)-based approach is adopted to optimize this fuzzy goal-programming model. An illustrative example is provided and some results of computational experiments are reported.

Computationally Efficient Sub-optimal Mid Course Guidance Using Model Predictive Static Programming (MPSP)

For a homing interceptor, suitable initial condition must be achieved by mid course guidance scheme for its maximum effectiveness. To achieve desired end goal of any mid course guidance scheme, two point boundary value problem must be solved online with all realistic constrain. A Newly developed computationally efficient technique named as MPSP (Model Predictive Static Programming) is utilized in this paper for obtaining suboptimal solution of optimal mid course guidance. Time to go uncertainty is avoided in this formulation by making use of desired position where midcourse guidance terminate and terminal guidance takes over. A suitable approach angle towards desired point also can be specified in this guidance law formulation. This feature makes this law particularly attractive because warhead effectiveness issue can be indirectly solved in mid course phase.

Register Allocation and Optimal Spill code Scheduling in Software Pipelined Loops using 0-1 Integer Linear Programming Formulation

In achieving higher instruction level parallelism, software pipelining increases the register pressure in the loop. The usefulness of the generated schedule may be restricted to cases where the register pressure is less than the available number of registers. Spill instructions need to be introduced otherwise. But scheduling these spill instructions in the compact schedule is a difficult task. Several heuristics have been proposed to schedule spill code. These heuristics may generate more spill code than necessary, and scheduling them may necessitate increasing the initiation interval. We model the problem of register allocation with spill code generation and scheduling in software pipelined loops as a 0-1 integer linear program. The formulation minimizes the increase in initiation interval (II) by optimally placing spill code and simultaneously minimizes the amount of spill code produced. To the best of our knowledge, this is the first integrated formulation for register allocation, optimal spill code generation and scheduling for software pipelined loops. The proposed formulation performs better than the existing heuristics by preventing an increase in II in 11.11% of the loops and generating 18.48% less spill code on average among the loops extracted from Perfect Club and SPEC benchmarks with a moderate increase in compilation time.