Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm

We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision “produces” a certain vector of “commodities”; it also has associated “traditional” queueing control effect, i.e., it determines traffic (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to find a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable.We introduce a dynamic control algorithm, which we call Greedy Primal-Dual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traffic sources and network processing nodes may be randomly time-varying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traffic rate constraints.     

A lexicographic minimax algorithm for multiperiod resource allocation

Resource allocation problems are typically formulated as mathematical programs with some special structure that facilitates the development of efficient algorithms. We consider a multiperiod problem in which excess resources in one period can be used in subsequent periods. The objective minimizes lexicographically the nonincreasingly sorted vector of weighted deviations of cumulative activity levels from cumulative demands. To this end, we first develop a new minimax algorithm that minimizes the largest weighted deviation among all cumulative activity levels. The minimax algorithm handles resource constraints, ordering constraints, and lower and upper bounds. At each iteration, it fixes certain variables at their lower bounds, and sets groups of other variables equal to each other as long as no lower bounds are violated. The algorithm takes advantage of the problem's special structure; e.g., each term in the objective is a linear decreasing function of only one variable. This algorithm solves large problems very fast, orders of magnitude faster than well known linear programming packages. (The latter are, of course, not designed to solve such minimax problems efficiently.) The lexicographic procedure repeatedly employs the minimax algorithm described above to solve problems, each of the same format but with smaller dimension.     

Fair resource allocation for different scenarios of demands

This paper considers a resource allocation problem, which objective is to treat fairly all the system users. Usually the requests cannot be entirely predicted, but the manager can forecast the request evolution, this leading to a set of possible scenarios. Such a problem arises for instance in network bandwidth allocation as well as in storage space management. It also appears in the management of computer systems, such as computational grids or in cloud computing, when teams share a common pool of machines. Problems of fair resource sharing arise among users with equal access right but with different needs.Here the problem is tackled by a multi-criteria model, where one criterion is associated to one scenario. A solution is a policy, which provides an allocation for each scenario. An algorithm is proposed and analysed that lists all solutions which are Pareto optimal with regard to the different possible user request scenarios. The algorithm is used offline, but can be adapted, with some additional hypothesis, to be used online.     

Approximation algorithms for dynamic resource allocation

We consider a problem of allocating limited quantities of M types of resources among N independent activities that evolve over T epochs. In each epoch, we assign to each activity a task which consumes resources, generates utility, and determines the subsequent state of the activity. We study the complexity of, and approximation algorithms for, maximizing average utility.     

Optimal resource allocation in survey designs

Resource allocation is a relatively new research area in survey designs and has not been fully addressed in the literature. Recently, the declining participation rates and increasing survey costs have steered research interests towards resource planning. Survey organizations across the world are considering the development of new mathematical models in order to improve the quality of survey results while taking into account optimal resource planning. In this paper, we address the problem of resource allocation in survey designs and we discuss its impact on the quality of the survey results. We propose a novel method in which the optimal allocation of survey resources is determined such that the quality of survey results, i.e., the survey response rate, is maximized. We demonstrate the effectiveness of our method by extensive numerical experiments.     

A branch and bound algorithm for dynamic resource allocation in population disease management

We embed an approximate dynamic program into a branch-and-bound framework to solve sequential resource allocation problems in population disease management. The proposed algorithm is capable of providing an optimality guarantee and getting bounds on the optimality gap of healthcare interventions. A numerical study on screening and treatment policy implementation for chronic hepatitis C virus (HCV) infection provides useful insights regarding HCV elimination for baby boomers.     

A distributed approach to capacity allocation in logical networks

We consider a dynamic capacity reallocation scheme in a logically fully-connected telecommunications network. We show that the problem of optimal capacity allocation can be solved in a distributed manner, an essential feature of such a scheme. Our continuous-capacity reallocation scheme can be used as a foundation for a discrete system. This is useful from the perspective of practical implementation.     

An exact algorithm for minimizing resource availability costs in project scheduling

A new exact algorithm that solves the Resource Availability Cost Problem (RACP) in project scheduling is shown to yield a significant improvement over the existing algorithm in the literature. The new algorithm consists of a hybrid method where an initial feasible solution is found heuristically. The branching scheme solves a Resource-Constrained Project Scheduling Problem (RCPSP) at each node where the resources of the RACP are fixed. The knowledge of previously solved RCPSPs is used to produce cuts in the search tree. A worst-case-performance theorem is established for this new algorithm. Experiments are performed on instances adapted from the PSPLIB database. The new algorithm can be used to minimize any resource availability cost problem once a procedure for the underlying resource-constrained problem is available.     

Modeling time allocation for prevention in primary care

This paper discusses the problem of allocating time for prevention at the primary care level, focusing on a general practitioner (GP) practice. The basic trade-off is between improved state of the health of the population, which translates into less demand for the GP services, and a decreased capacity for curative services, which translates into increased congestion. The problem of how much time to devote to prevention is modeled as a non-linear optimization problem. As an extension of the problem, selection of preventive activities to perform among recommended alternatives is modeled using a knapsack formulation, and its application is illustrated with a numerical example. The author is supported in part by Türkiye Bilimsel ve Teknik Araştirma Kurumu (TüBİTAK) Career Grant No. 106K260.     

An effective ant colony optimization algorithm (ACO) for multi-objective resource allocation problem (MORAP)

The multi-objective resource allocation problem (MORAP) addresses the important issue which seeks to find the expected objectives by allocating the limited amount of resource to various activates. Resources may be manpower, assets, raw material or anything else in limited supply which can be used to accomplish the goals. The goals may be objectives (i.e., minimizing costs, or maximizing efficiency) usually driven by specific future needs. In this paper, in order to obtain a set of Pareto solution efficiently, we proposed a modified version of ant colony optimization (ACO), in this algorithm we try to increase the efficiency of algorithm by increasing the learning of ants. Effectiveness and efficiency of proposed algorithm was validated by comparing the result of ACO with hybrid genetic algorithm (hGA) which was applied to MORAP later.     

Stochastic models for strategic resource allocation in nonprofit foreclosed housing acquisitions

Increased rates of mortgage foreclosures in the U.S. have had devastating social and economic impacts during and after the 2008 financial crisis. As part of the response to this problem, nonprofit organizations such as community development corporations (CDCs) have been trying to mitigate the negative impacts of mortgage foreclosures by acquiring and redeveloping foreclosed properties. We consider the strategic resource allocation decisions for these organizations which involve budget allocations to different neighborhoods under cost and return uncertainty. Based on interactions with a CDC, we develop stochastic integer programming based frameworks for this decision problem, and assess the practical value of the models by using real-world data. Both policy-related and computational analyses are performed, and several insights such as the trade-offs between different objectives, and the efficiency of different solution approaches are presented.     

Lower bound for the mean project completion time in dynamic PERT networks

We apply the stochastic dynamic programming to obtain a lower bound for the mean project completion time in a PERT network, where the activity durations are exponentially distributed random variables. Moreover, these random variables are non-static in that the distributions themselves vary according to some randomness in society like strike or inflation. This social randomness is modelled as a function of a separate continuous-time Markov process over the time horizon. The results are verified by simulation.     

Optimal algorithms for page migration in dynamic networks

We present an extension of a classical data management subproblem, the page migration. The problem is investigated in dynamic networks, where costs of communication between different nodes may change with time. We construct asymptotically optimal online algorithms for this problem, both in deterministic and randomized scenarios.     

A unified approach for scheduling with convex resource consumption functions using positional penalties

We provide a unified model for solving single machine scheduling problems with controllable processing times in polynomial time using positional penalties. We show how this unified model can be useful in solving three different groups of scheduling problems. The first group includes four different due date assignment problems to minimize an objective function which includes costs for earliness, tardiness, due date assignment, makespan and total resource consumption. The second group includes three different due date assignment problems to minimize an objective function which includes the weighted number of tardy jobs, due date assignment costs, makespan and total resource consumption costs. The third group includes various scheduling problems which do not involve due date assignment decisions. We show that each of the problems from the first and the third groups can be reduced to a special case of our unified model and thus can be solved in O(n³)$O(n^3)$ time. Furthermore, we show how the unified model can be used repeatedly as a subroutine to solve all problems from the second group in O(n⁴)$O(n^4)$ time. In addition, we also show that faster algorithms exist for several special cases.     

A Monte Carlo algorithm for real time task scheduling on multi-core processors with software controlled dynamic voltage scaling

The task scheduling problem for multi-core processors is an important algorithm design issue. Dynamic voltage scaling (DVS) is used to reduce the energy consumption of cores. We ponder the problem of task scheduling on a multi-core processor with software controlled DVS where the objective is to reduce the energy consumption. We consider a system with a single multi-core processor with software controlled DVS having a finite set of core speeds and discuss a task scheduling problem associated with it. The problem that we address is to find a minimum energy task schedule for a given set of independent tasks that have to be completed within a given common deadline. We propose a Monte Carlo algorithm of complexity $O(t(\mathit{mp}+q+\mathit{log}(t))+p(t+q)(D^{\mathit{pq}}+n))$ for solving the task scheduling problem and compare it with the optimal algorithm. Here t is the number of tasks, p is the number of cores, q is the number of core speeds, m is an integer parameter that is the number of iterations we should try to get a feasible solution before declaring that no solution is possible, n is an integer parameter that is the number of iterations we should try to reduce the energy consumption when we get a feasible solution, and D is the common deadline of the tasks.     

Optimal procedures for the discrete time/cost trade-off problem in project networks

We describe two algorithms, based on dynamic programming logic, for optimally solving the discrete time/cost trade-off problem (DTCTP) in deterministic activity-on-arc networks of the CPM type, where the duration of each activity is a discrete, nonincreasing function of the amount of a single nonrenewable resource committed to it. The first algorithm is based on a procedure proposed by Bein, Kamburowski and Stallmann for finding the minimal number of reductions necessary to transform a general network to a series-parallel network. The second algorithm minimizes the estimated number of possibilities that need to be considered during the solution procedure. Both procedures have been programmed in C and tested on a large set of representative networks to give a good indication of their performance, and indicate the circumstances in which either algorithm performs best.     

A new multi-objective self-organizing optimization algorithm (MOSOA) for spatial optimization problems

Spatial planning is an important and complex activity. It includes land use planning and resource allocation as basic components. An abundance of papers can be found in the literature related to each one of these two aspects separately. On the contrary, a much smaller number of research reports deal with both aspects simultaneously. This paper presents an innovative evolutionary algorithm for treating combined land use planning and resource allocation problems. The new algorithm performs optimization on a cellular automaton domain, applying suitable transition rules on the individual neighbourhoods. The optimization process is multi-objective, based on non-domination criteria and self-organizing. It produces a Pareto front thus offering an advantage to the decision maker, in comparison to methods based on weighted-sum objective functions. Moreover, the present multi-objective self-organizing algorithm (MOSOA) can handle both local and global spatial constraints. A combined land use and water allocation problem is treated, in order to illustrate the cellular automaton optimization approach. Water is allocated after pumping from an aquifer, thus contributing a nonlinearity to the objective function. The problem is bi-objective aiming at (a) the minimization of soil and groundwater pollution and (b) the maximization of economic profit. An ecological and a socioeconomic constraint are imposed: (a) Groundwater levels at selected places are kept above prescribed thresholds. (b) Land use quota is predefined. MOSOA is compared to a standard multi-objective genetic algorithm and is shown to yield better results both with respect to the Pareto front and to the degree of compactness. The latter is a highly desirable feature of a land use pattern. In the land use literature, compactness is part of the objective function or of the constraints. In contrast, the present approach renders compactness as an emergent result.     

A dynamic genetic algorithm based on continuous neural networks for a kind of non-convex optimization problems

This paper presents a kind of dynamic genetic algorithm based on a continuous neural network, which is intrinsically the steepest decent method for constrained optimization problems. The proposed algorithm combines the local searching ability of the steepest decent methods with the global searching ability of genetic algorithms. Genetic algorithms are used to decide each initial point of the steepest decent methods so that all the initial points can be searched intelligently. The steepest decent methods are employed to decide the fitness of genetic algorithms so that some good initial points can be selected. The proposed algorithm is motivated theoretically and biologically. It can be used to solve a non-convex optimization problem which is quadratic and even more non-linear. Compared with standard genetic algorithms, it can improve the precision of the solution while decreasing the searching scale. In contrast to the ordinary steepest decent method, it can obtain global sub-optimal solution while lessening the complexity of calculation.     

Resource allocation for end-to-end QoS provisioning in a hybrid wireless WCDMA and wireline IP-based DiffServ network

In the future UMTS network, the heterogeneous traffics of multimedia services demand various QoS provisioning. At the same time, the seamlessly conveying of information between mobile users and a hybrid network requires the networking from wireless to wireline domains. However, in both academia and industries, the end-to-end QoS provisioning in the integration of wireline and wireless networks remains a challenge. In this paper, a modeling of a hybrid wireless WCDMA and wireline IP-based DiffServ network is presented to investigate the resource allocation for end-to-end QoS provisioning for multimedia services. In the wireless domain, the mathematical modeling of the cross-layer model including the physical layer, the link layer and the network layer is built. The connection admission control scheme is implemented based on the cross-layer model to determine the amount of resource for different services. In the wireline domain, we define the mapping of QoS classes between UMTS and DiffServ networks according to different QoS requirements. We propose a bandwidth allocation scheme to provide satisfactory packet loss and delay guarantee in DiffServ networks. The final end-to-end admission control scheme combines the resource allocation and admission control in both wireless and wireline domains. The analytical and simulation results show that the proposed resource allocation and admission control schemes work cooperatively in the presented hybrid wireless and wireline networks to guarantee the end-to-end QoS requirements for multimedia services.     

Improved algorithm for broadcast scheduling of minimal latency in wireless ad hoc networks

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. One of the key communication operations is to broadcast a message from a source node. This paper studies the minimum latency broadcast scheduling problem in wireless ad hoc networks under collision-free transmission model. The previously best known algorithm for this NP-hard problem produces a broadcast schedule whose latency is at least 648（rmax/rmin）^2 times that of the optimal schedule, where rmax and rmin are the maximum and minimum transmission ranges of nodes in a network, respectively. We significantly improve this result by proposing a new scheduling algorithm whose approximation performance ratio is at most （1 ＋ 2rmax/rmin）^2＋32, Moreover, under the proposed scheduling each node just needs to forward a message at most once.