Analysis of a trunk reservation policy in the framework of fog computing

We analyze in this paper a system composed of two data centers with limited capacity in terms of servers. When one request for a single server is blocked at the first data center, this request is forwarded to the second one. To protect the single server requests originally assigned to the second data center, a trunk reservation policy is introduced (i.e., a redirected request is accepted only if there is a sufficient number of free servers at the second data center). After rescaling the system by assuming that there are many servers in both data centers and high request arrival rates, we are led to analyze a random walk in the quarter plane, which has the particularity of having non constant reflecting conditions on one boundary of the quarter plane. Contrary to usual reflected random walks, to compute the stationary distribution of the presented random walk, we have to determine three unknown functions, one polynomial and two infinite generating functions. We show that the coefficients of the polynomial are solutions to a linear system. After solving this linear system, we are able to compute the two other unknown functions and the blocking probabilities at both data centers. Numerical experiments are eventually performed to estimate the gain achieved by the trunk reservation policy

Call blocking probabilities for Poisson traffic under the Multiple Fractional Channel Reservation policy

In this paper, we study the performance of the Multiple Fractional Channel Reservation (MFCR) policy, which is a bandwidth reservation policy that allows the reservation of real (not integer) number of channels in order to favor calls of high channel (bandwidth) requirements. We consider a link of fixed capacity that accommodates Poisson arriving calls of different service-classes with different bandwidth-per-call requirements. Calls compete for the available bandwidth under the MFCR policy. To determine call blocking probabilities, we propose approximate but recursive formulas based on the notion of reserve transition rates. The accuracy of the proposed method is verified through simulation

Provably Near-Optimal LP-Based Policies for Revenue Management in Systems with Reusable Resources

Motivated by emerging applications in workforce management, we consider a class of revenue management problems in systems with reusable resources. The corresponding applications are modeled using the well-known loss network systems. We use an extremely simple linear program (LP) that provides an upper bound on the best achievable expected long-run revenue rate. The optimal solution of the LP is used to devise a conceptually simple control policy that we call the class selection policy (CSP). Moreover, the LP is used to analyze the performance of the CSP policy. We obtain the _rst control policy with uniform performance guarantees. In particular, for the model with single resource and uniform resource requirements, the CSP policy is guaranteed to have expected long-run revenue rate that is at least half of the best achievable. More generally, as the ratio between the capacity of the system and the maximum resource requirement grows to in_nity, the CSP policy is asymptotically optimal, regardless of any other parameter of the problem. The asymptotic performance analysis that we obtain is more general than existing results in several important dimensions. It is based on several novel ideas that we believe will be useful in other settings

Dynamic routing in circuit-switched non-hierarchical networks

This thesis studies dynamic routing in circuit-switched non-hierarchical networks based on learning automata algorithms. The application of a mathematical model for a linear reward penalty algorithm is explained. Theoretical results for this scheme verified by simulations shows the accuracy of the model. Using simulation and analysis, learning automata algorithms are compared to several other strategies on different networks. The implemented test networks may be classified into two groups. The first group are designed for fixed routing and in such networks fixed routing performs better than any dynamic routing scheme. It will be shown that dynamic routing strategies perform as well as fixed routing when trunk reservation is employed. The second group of networks are designed for dynamic routing and trunk reservation deteriorates the performance. Comparison of different routing algorithms on small networks designed to force dynamic routing demonstrates the superiority of automata under both normal and failure conditions. The thesis also considers the instability problem in non-hierarchical circuit-switched networks when dynamic routing is implemented. It is shown that trunk reservation prevents instability and increases the carried load at overloads. Finally a set of experiments are performed on large networks with realistic capacity and traffic matrices. Simulation and analytic results show that dynamic routing outperforms fixed routing and trunk reservation deteriorates the performance at low values of overload. At high overloads, optimization of trunk reservation is necessary for this class of networks. Comparison results show the improved performance with automata schemes under both normal and abnormal traffic conditions. The thesis concludes with a discussion of proposed further work including expected developments in Integrated Service Digital Networks

Improved learning automata applied to routing in multi-service networks

Multi-service communications networks are generally designed, provisioned and configured, based on source-destination user demands expected to occur over a recurring time period. However due to network users' actions being non-deterministic, actual user demands will vary from those expected, potentially causing some network resources to be under- provisioned, with others possibly over-provisioned. As actual user demands vary over the recurring time period from those expected, so the status of the various shared network resources may also vary. This high degree of uncertainty necessitates using adaptive resource allocation mechanisms to share the finite network resources more efficiently so that more of actual user demands may be accommodated onto the network. The overhead for these adaptive resource allocation mechanisms must be low in order to scale for use in large networks carrying many source-destination user demands. This thesis examines the use of stochastic learning automata for the adaptive routing problem (these being adaptive, distributed and simple in implementation and operation) and seeks to improve their weakness of slow convergence whilst maintaining their strength of subsequent near optimal performance. Firstly, current reinforcement algorithms (the part causing the automaton to learn) are examined for applicability, and contrary to the literature the discretised schemes are found in general to be unsuitable. Two algorithms are chosen (one with fast convergence, the other with good subsequent performance) and are improved through automatically adapting the learning rates and automatically switching between the two algorithms. Both novel methods use local entropy of action probabilities for determining convergence state. However when the convergence speed and blocking probability is compared to a bandwidth-based dynamic link-state shortest-path algorithm, the latter is found to be superior. A novel re-application of learning automata to the routing problem is therefore proposed: using link utilisation levels instead of call acceptance or packet delay. Learning automata now return a lower blocking probability than the dynamic shortest-path based scheme under realistic loading levels, but still suffer from a significant number of convergence iterations. Therefore the final improvement is to combine both learning automata and shortest-path concepts to form a hybrid algorithm. The resulting blocking probability of this novel routing algorithm is superior to either algorithm, even when using trend user demands

Revenue Management of Reusable Resources with Advanced Reservations

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/1/poms12672_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/2/poms12672.pd

Optimal admission policies for small star networks

In this thesis admission stationary policies for small Symmetric Star telecommunication networks in which there are two types of calls requesting access are considered. Arrivals form independent Poisson streams on each route. We consider the routing to be fixed. The holding times of the calls are exponentially distributed periods of time. Rewards are earned for carrying calls and future returns are discounted at a fixed rate. The operation of the network is viewed as a Markov Decision Process and we solve the optimality equation for this network model numerically for a range of small examples by using the policy improvement algorithm of Dynamic Programming. The optimal policies we study involve acceptance or rejection of traffic requests in order to maximise the Total Expected Discounted Reward. Our Star networks are in some respect the simplest networks more complex than single links in isolation but even so only very small examples can be treated numerically. From those examples we find evidence that suggests that despite their complexity, optimal policies have some interesting properties. Admission Price policies are also investigated in this thesis. These policies are not optimal but they are believed to be asymptotically optimal for large networks. In this thesis we investigate if such policies are any good for small networks; we suggest that they are. A reduced state-space model is also considered in which a call on a 2-link route, once accepted, is split into two independent calls on the links involved. This greatly reduces the size of the state-space. We present properties of the optimal policies and the Admission Price policies and conclude that they are very good for the examples considered. Finally we look at Asymmetric Star networks with different number of circuits per link and different exponential holding times. Properties of the optimal policies as well as Admission Price policies are investigated for such networks

Simulation and analysis of adaptive routing and flow control in wide area communication networks

This thesis presents the development of new simulation and analytic models for the performance analysis of wide area communication networks. The models are used to analyse adaptive routing and flow control in fully connected circuit switched and sparsely connected packet switched networks. In particular the performance of routing algorithms derived from the L(_R-I) linear learning automata model are assessed for both types of network. A novel architecture using the INMOS Transputer is constructed for simulation of both circuit and packet switched networks in a loosely coupled multi- microprocessor environment. The network topology is mapped onto an identically configured array of processing centres to overcome the processing bottleneck of conventional Von Neumann architecture machines. Previous analytic work in circuit switched work is extended to include both asymmetrical networks and adaptive routing policies. In the analysis of packet switched networks analytic models of adaptive routing and flow control are integrated to produce a powerful, integrated environment for performance analysis The work concludes that routing algorithms based on linear learning automata have significant potential in both fully connected circuit switched networks and sparsely connected packet switched networks

Neural networks applied to traffic management in telephone networks

In this paper the application of neural networks to some of the network management tasks carried out in a regional Bell telephone company is described. Network managers monitor the telephone network for abnormal conditions and have the ability to place controls in the network to improve traffic flow. Conclusions are drawn regarding the utility and effectiveness of the neural networks in automating the network management tasks