Efficient estimation of blocking probabilities in non-stationary loss networks

This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method

Stochastische Analyse und lernbasierte Algorithmen zur Ressourcenbereitstellung in optischen Netzwerken

The unprecedented growth in Internet traffic has driven the innovations in provisioning of optical resources as per the need of bandwidth demands such that the resource utilization and spectrum efficiency could be maximized. With the advent of the next generation flexible optical transponders and switches, the flexible-grid-based elastic optical network (EON) is foreseen as an alternative to the widely deployed fixed-grid-based wavelength division multiplexing networks. At the same time, the flexible resource provisioning also raises new challenges for EONs. One such challenge is the spectrum fragmentation. As network traffic varies over time, spectrum gets fragmented due to the setting up and tearing down of non-uniform bandwidth requests over aligned (i.e., continuous) and adjacent (i.e., contiguous) spectrum slices, which leads to a non-optimal spectrum allocation, and generally results in higher blocking probability and lower spectrum utilization in EONs. To address this issue, the allocation and reallocation of optical resources are required to be modeled accurately, and managed efficiently and intelligently. The modeling of routing and spectrum allocation in EONs with the spectrum contiguity and spectrum continuity constraints is well-investigated, but existing models do not consider the fragmentation issue resulted by these constraints and non-uniform bandwidth demands. This thesis addresses this issue and considers both the constraints to computing exact blocking probabilities in EONs with and without spectrum conversion, and with spectrum reallocation (known as defragmentation) for the first time using the Markovian approach. As the exact network models are not scalable with respect to the network size and capacity, this thesis proposes load-independent and load-dependent approximate models to compute approximate blocking probabilities in EONs. Results show that the connection blocking due to fragmentation can be reduced by using a spectrum conversion or a defragmentation approach, but it can not be eliminated in a mesh network topology. This thesis also deals with the important network resource provisioning task in EONs. To this end, it first presents algorithmic solutions to efficiently allocate and reallocate spectrum resources using the fragmentation factor along spectral, time, and spatial dimensions. Furthermore, this thesis highlights the role of machine learning techniques in alleviating issues in static provisioning of optical resources, and presents two use-cases: handling time-varying traffic in optical data center networks, and reducing energy consumption and allocating spectrum proportionately to traffic classes in fiber-wireless networks.Die flexible Nutzung des Spektrums bringt in Elastischen Optischen Netze (EON) neue Herausforderungen mit sich, z.B., die Fragmentierung des Spektrums. Die Fragmentierung entsteht dadurch, dass die Netzwerkverkehrslast sich im Laufe der Zeit ändert und so wird das Spektrum aufgrund des Verbindungsaufbaus und -abbaus fragmentiert. Das für eine Verbindung notwendige Spektrum wird durch aufeinander folgende (kontinuierliche) und benachbarte (zusammenhängende) Spektrumsabschnitte (Slots) gebildet. Dies führt nach den zahlreichen Reservierungen und Freisetzungen des Spektrums zu einer nicht optimalen Zuordnung, die in einer höheren Blockierungs-wahrscheinlichkeit der neuen Verbindungsanfragen und einer geringeren Auslastung von EONs resultiert. Um dieses Problem zu lösen, müssen die Zuweisung und Neuzuordnung des Spektrums in EONs genau modelliert und effizient sowie intelligent verwaltet werden. Diese Arbeit beschäftigt sich mit dem Fragmentierungsproblem und berücksichtigt dabei die beiden Einschränkungen: Kontiguität und Kontinuität. Unter diesen Annahmen wurden analytische Modelle zur Berechnung einer exakten Blockierungswahrscheinlichkeit in EONs mit und ohne Spektrumskonvertierung erarbeitet. Außerdem umfasst diese Arbeit eine Analyse der Blockierungswahrscheinlichkeit im Falle einer Neuzuordnung des Sprektrums (Defragmentierung). Diese Blockierungsanalyse wird zum ersten Mal mit Hilfe der Markov-Modelle durchgeführt. Da die exakten analytischen Modelle hinsichtlich der Netzwerkgröße und -kapazität nicht skalierbar sind, werden in dieser Dissertation verkehrslastunabhängige und verkehrslastabhängige Approximationsmodelle vorgestellt. Diese Modelle bieten eine Näherung der Blockierungswahrscheinlichkeiten in EONs. Die Ergebnisse zeigen, dass die Blockierungswahrscheinlichkeit einer Verbindung aufgrund von einer Fragmentierung des Spektrums durch die Verwendung einer Spektrumkonvertierung oder eines Defragmentierungsverfahrens verringert werden kann. Eine effiziente Bereitstellung der optischen Netzwerkressourcen ist eine wichtige Aufgabe von EONs. Deswegen befasst sich diese Arbeit mit algorithmischen Lösungen, die Spektrumressource mithilfe des Fragmentierungsfaktors von Spektral-, Zeit- und räumlichen Dimension effizient zuweisen und neu zuordnen. Darüber hinaus wird die Rolle des maschinellen Lernens (ML) für eine verbesserte Bereitstellung der optischen Ressourcen untersucht und das ML basierte Verfahren mit der statischen Ressourcenzuweisung verglichen. Dabei werden zwei Anwendungsbeispiele vorgestellt und analysiert: der Umgang mit einer zeitveränderlichen Verkehrslast in optischen Rechenzentrumsnetzen, und eine Verringerung des Energieverbrauchs und die Zuweisung des Spektrums proportional zu Verkehrsklassen in kombinierten Glasfaser-Funknetzwerken

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably\ud (i) classical circuit switch telephone networks (loss networks) and\ud (ii) present-day wireless mobile networks.\ud \ud Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it has not in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hyper cubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to\ud \ud - secure upper bounds for loss probabilities and\ud - analytic error bounds for the accuracy of the approximation for various performance measures.\ud \ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud \ud - pure loss networks as under (i)\ud - GSM-networks with fixed channel allocation as under (ii).\ud \ud The results are of practical interest for computational simplifications and, particularly, to guarantee blocking probabilities not to exceed a given threshold such as for network dimensioning.\u

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are (i) classical circuit switch telephone networks (loss networks) and (ii) present-day wireless mobile networks. Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it does not have one in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hypercubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to (1) upper bounds for loss probabilities and \ud (2) analytic error bounds for the accuracy of the approximation for various performance measures.\ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud (1)• pure loss networks as under (2)• GSM networks with fixed channel allocation as under.\ud The results are of practical interest for computational simplifications and, particularly, to guarantee that blocking probabilities do not exceed a given threshold such as for network dimensioning

Performance Analysis and Design of Mobile Ad-Hoc Networks

We focus on the performance analysis and design of a wireless ad-hoc network using a virtual-circuit or reservation based medium access layer. In a reservation based MAC network, source nodes reserve a session's link capacity end-to-end over the entire path before sending traffic over the established path. An example of a generic reservation based MAC protocol is Unifying Slot Assignment Protocol (USAP). Any reservation based medium access protocol (including USAP) uses a simple set of rules to determine the cells or timeslots available at a node to reserve link capacity along the path to the next node. Given inputs of node locations, traffic pattern between nodes and link propagation matrices, we develop models to estimate blocking probability and throughput for reservation based wireless ad-hoc networks. These models are based on extending reduced load loss network models for a wireless network. For generic USAP with multiple frequency channels, the key effect of multiuser interference on a link is modeled via reduced available link capacity where the effects of transmissions and receptions in the link neighborhood are modeled using USAP reservation rules. We compare our results with simulation and obtain good results using our extended reduced load loss network models but with reduced available link capacity distribution obtained by simulation. For the case of generic USAP using a single frequency channel, we develop models for unicast traffic using reduced load loss network models but with the sharing of the wireless medium between a node and its neighbors modeled by considering cliques of neighboring interfering links around a particular link. We compare results of this model with simulation and show good match. We also develop models to calculate source-destination throughput for the reservation MAC as used in the Joint Tactical Radio System to support both unicast and multicast traffic. These models are based on extending reduced load loss network models for wireless multicast traffic with the sharing of the wireless medium between a node and its (upto 2 hop) neighbors modeled by considering cliques of interfering nodes around a particular node. We compare results of this model with simulation and show good match with simulation. Once we have developed models to estimate throughput and blocking probabilities, we use these models to optimize total network throughput. In order to optimize total throughput, we compute throughput sensitivities of the reduced load loss network model using an implied cost formulation and use these sensitivities to choose the routing probabilities among multiple paths so that total network throughput is maximized. In any network scenario, MANETs can get disconnected into clusters. As part of the MANET design problem, we look at the problem of establishing network connectivity and satisfying required traffic capacity between disconnected clusters by placing a minimum number of advantaged high flying Aerial Platforms (APs) as relay nodes at appropriate places. We also extend the connectivity solution in order to make the network single AP survivable. The problem of providing both connectivity and required capacity between disconnected ground clusters (which contain nodes that can communicate directly with each other) is formulated as a summation-form clustering problem of the ground clusters with the APs along with inter-AP distance constraints that make the AP network connected and with complexity costs that take care of ground cluster to AP capacity constraints. The resultant clustering problem is solved using Deterministic Annealing to find (near) globally optimal solutions for the minimum number and locations of the APs to establish connectivity and provide required traffic capacity between disconnected clusters. The basic connectivity constraints are extended to include conditions that make the resultant network survivable to a single AP failure. In order to make the network single AP survivable, we extend the basic connectivity solution by adding another summation form constraint so that the AP network forms a biconnected network and also by making sure that each ground cluster is connected to atleast two APs. We establish the validity of our algorithms by comparing them with optimal exhaustive search algorithms and show that our algorithms are near-optimal for the problem of establishing connectivity between disconnected clusters

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

A heuristic for placement of limited range wavelength converters in all-optical networks

Wavelength routed optical networks have emerged as a technology that can effectively utilize the enormous bandwidth of the optical fiber. Wavelength converters play an important role in enhancing the fiber utilization and reducing the overall call blocking probability of the network. As the distortion of the optical signal increases with the increase in the range of wavelength conversion in optical wavelength converters, limited range wavelength conversion assumes importance. Placement of wavelength converters is a NP complete problem [K.C. Lee, V.O.K. Li, IEEE J. Lightwave Technol. 11 (1993) 962-970] in an arbitrary mesh network. In this paper, we investigate heuristics for placing limited range wavelength converters in arbitrary mesh wavelength routed optical networks. The objective is to achieve near optimal placement of limited range wavelength converters resulting in reduced blocking probabilities and low distortion of the optical signal. The proposed heuristic is to place limited range wavelength converters at the most congested nodes, nodes which lie on the long lightpaths and nodes where conversion of optical signals is significantly high. We observe that limited range converters at few nodes can provide almost the entire improvement in the blocking probability as the full range wavelength converters placed at all the nodes. Congestion control in the network is brought about by dynamically adjusting the weights of the channels in the link thereby balancing the load and reducing the average delay of the traffic in the entire network. Simulations have been carried out on a 12-node ring network, 14-node NSFNET, 19-node European Optical Network (EON), 28-node US long haul network, hypothetical 30-node INET network and the results agree with the analysis. (C) 2001 Elsevier Science B.V, All rights reserved