Loss circuit switched communication network-performance analysis and dynamic routing

We investigate a loss circuit switched communication network with state-dependent dynamic routing strategy, wherein the state of the network at the time of call arrival determines whether or not the call is accepted and, if accepted, its route. We develop an approximate approach to the network performance analysis. The approach enhances the Fixed Point Model by treating multiple solutions of the Fixed Point Equations. Assuming that the multiple solutions correspond to the long-living network modes, we develop the aggregated Markov chain that describes the network transitions among these modes. We also propose and discuss a new state-dependent dynamic routing strategy which we call Least-Expected-Blocking strategy (LEB). LEB accepts an incoming call only if this results in a decrease in the expected blocking probability and it chooses a route that yields the maximum decrease. The new strategy outperforms the previously known strategies by the criterion of network steady blocking probability.     

Robust delay-constrained routing in telecommunications

In telecommunications, operators usually use market surveys and statistical models to estimate traffic evolution in networks or to approximate queuing delay functions in routing strategies. Many research activities concentrated on handling traffic uncertainty in network design. Measurements on real world networks have shown significant errors in delay approximations, leading to weak management decisions in network planning. In this work, we introduce elements of robust optimization theory for delay modeling in routing problems. Different types of data uncertainty are considered and linked to corresponding robust models. We study a special case of constraints featuring separable additive functions. Specifically, we consider that each term of the sum is disturbed by a random parameter. These constraints are frequent in network based problems, where functions reflecting real world measurements on links are summed up over end-to-end paths. While classical robust formulations have to deal with the introduction of new variables, we show that, under specific hypotheses, the deterministic robust counterpart can be formulated in the space of original variables. This offers the possibility of constructing tractable robust models. Starting from Soyster’s conservative model, we write and compare different uncertainty sets and formulations offering each a different protection level for the delay constrained routing problem. Computational experiments are developed in order to evaluate the “price of robustness” and to assess the quality of the new formulations.     

Multipolar routing: where dynamic and static routing meet

Assuming that the traffic matrix belongs to a polytope, we describe a new routing paradigm where each traffic matrix is routed a combination of a number of extreme routings. This combination depends on the current traffic matrix. Multipolar routing can be seen as a generalization of both routing and robust static routing. Moreover, the time complexity of multipolar routing is under control since it depends on the number of poles (i.e. the number of extreme routings) which can be defined by the network planner     

Congestion control using dynamic routing and flow control

In this paper, the congestion control in store and forward computer com-munication networks is studied, the method employed consists of a combination of a dynamic routing policy that minimizes the delay, and buffer nianagement schemes to control the flow of data. Simulation using liner programming has been carried out, under balanced and transient traffic conditions, on a simple 3–node network , the relative merits and drawbacks of each approach are discussed. Irland [2], showed that with static routing, the SQRT scheme improves the switch performance. In this paper it is shown that in the case of dynamic routing, the SQRT is an excellent solution to remedy the performance degradation caused by CP and CS schemes     

Call admission control schemes and ATM network topological design

Call admission control criteria are not only important for call admission control itself, but also can be an important input to network topological design. In this paper, we show the difference in terms of network cost incurred by adopting different call admission control schemes in network topological design. We compare two call admission control schemes. Scheme 1 uses equivalent bandwidth as its call admission control criterion and Scheme 2 is based on modeling the volatility of call traffic using Reflected Brownian Motion. Though Scheme 2 increases the complexity of network topological design, it can give lower network costs. Our experimental results show that for the same traffic mix, the network cost can be as little as 10% and as much as 35% lower when Scheme 2 is used instead of Scheme 1. The differences between the pair of resulting networks suggests that network topological design can be used as one of the criteria for choosing the call admission control scheme.     

Simulating vehicular traffic in a network using dynamic routing

We present a new numerical code which solves the Lighthill – Whitham model, the classic macroscopic model for vehicular traffic flow, in a network with multi-destinations. We use a high-resolution shock-capturing scheme with approximate Riemann solver to solve the partial differential equations of the Lighthill – Whitham theory. These schemes are very efficient, robust and moreover well adapted to simulations of traffic flows. We develop a theory of dynamic routing including a procedure for traffic flow assignment at junctions which reproduces the correct propagation of irregularities and ensures at the same time conservation of the number of vehicles.     

Impact of source load and routing on QoS of packets delivery

We study how the number of packets in transit (NPT), that is an aggregate measure of a network quality of service (QoS) performance, is affected by routing algorithm coupled with volume of incoming traffic. We use our simulation model that is an abstraction of the Network Layer of the OSI Reference Model. We consider a static routing and two different types of dynamic routings and different volumes of incoming traffic in the network free flow state. Our study shows that the efficiency of performance of a routing changes with the volume of incoming traffic among the considered routings.     

Optimal evacuation planning using staging and routing

Evacuation is an important disaster management tool. Evacuating a large region by automobile (the most commonly used mode) is a difficult task, especially as high levels of traffic congestion often form. This paper studies the use of demand-based strategies, specifically, the staging and routing of evacuees. These strategies attempt to manage demand in order to reduce or eliminate congestion. A strategic mixed-integer programming planning model that accounts for evacuation dynamics and congestion is used to study these strategies. The strategies adopted incorporate different evacuee types based on destination requirements and shelter capacity restrictions. The main objective studied is to minimize the network clearance time. We examine the structure of optimal strategies, yielding insights into the use of staging and routing in evacuation management. These insights are then used to develop effective solution procedures. To demonstrate the efficacy of the proposed solution technique, we provide computational experience using a large realistic example based on Virginia Beach.     

A meta-model for multiobjective routing in MPLS networks

MPLS (Multiprotocol Label Switching) enables the utilisation of explicit routes and other advanced routing mechanisms in multiservice packet networks, capable of dealing with multiple and heterogeneous QoS (Quality of Service) parameters. Firstly the paper presents a discussion of conceptual and methodological issues raised by multiobjective routing optimisation models for MPLS networks. The major contribution is the proposal of a multiobjective routing optimisation framework for MPLS networks. The major features of this modelling framework are: the formulation of a three-level hierarchical routing optimisation problem including network and service performance objectives, the inclusion of fairness objectives in the different levels of optimisation and a two-level stochastic representation of the traffic in the network (traffic flow and packet stream levels). A variant of the general model for two classes of traffic flows, QoS traffic and Best Effort traffic, is also presented. Finally a stochastic teletraffic modelling approach, underlying the optimisation model, is fully described. Work partially supported by programme POSI of the III EC programme cosponsored by FEDER and national funds.     

Fluid models of integrated traffic and multipath routing

In this paper we consider a stochastic model describing the varying number of flows in a network. This model features flows of two types, namely file transfers (with fixed volume) and streaming traffic (with fixed duration), and extends the model of Key, Massoulié, Bain and Kelly [27] by allowing more general bandwidth allocation criteria. We analyse the dynamics of the system under a fluid scaling, and show Lyapunov stability of the fluid limits under a natural stability condition. We provide natural interpretations of the fixed points of these fluid limits. We then compare the fluid dynamics of file transfers under (i) balanced multipath routing and (ii) parallel, uncoordinated routing. We show that for identical traffic demands, parallel uncoordinated routing can be unstable while balanced multipath routing is stable. Finally, we identify multi-dimensional Ornstein-Uhlenbeck processes as second-order approximations to the first-order fluid limit dynamics.     

Multi-layered round robin routing for parallel servers

We study a system of several identical servers in parallel, where a routing decision must be made immediately on a job’s arrival. Jobs arrive according to a Poisson process, with their processing times following a discrete distribution with finite support. The processing time of a job is known on arrival and may be used in the routing decision. We propose a policy consisting of multi-layered round robin routing followed by shortest remaining processing time scheduling at the servers. This policy is shown to have a heavy traffic limit that is identical to one in which there is a single queue (no routing) and optimal heavy traffic scheduling. In light traffic, we show that the performance of this policy is worse than round robin routing followed by shortest remaining processing time scheduling. We also quantify the difference between round robin and multi-layered round robin routing, which in turn yields insights on the relative importance of routing versus (local) scheduling in such systems. AMS subject classifications: 68M20 · 60K25 (Work done while both authors were visitors at EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.)     

Energy aware proactive optimized link state routing in mobile ad-hoc networks

In this paper we develop a novel energy aware routing approach for mobile ad hoc network (MANET) problems. The approach is based on using Optimized Link State Routing Protocol. Our Energy Aware OLSR labeled as OLSR_EA measures and predicts per-interval energy consumptions using the well-known Auto-Regressive Integrated Moving Average time series method. We develop a composite energy cost, by considering transmission power consumption and residual energy of each node, and use this composite energy index as the routing metric. Our extensive ns2 simulation experiments show that OLSR_EA substantially prolongs the network lifetime and saves total energy used in MANET. In our experiments we considered different scenarios considering a variety of traffic loads, node mobilities, homogeneous power consumption, and heterogeneous power consumption. Simulation results also confirm that OLSR_EA improves the traffic balance between nodes, and packet delivery ratio in higher node speed. We further develop characteristics of OLSR_EA in power-wise heterogeneous MANET to achieve efficient energy preserving performance.     

Jittering performance of random deflection routing in packet networks

This paper reports a study of random deflection routing protocol and its impact on delay-jitter over packet networks. In case of congestion, routers with a random deflection routing protocol can forward incoming packets to links laying off shortest paths; namely, packets can be “deflected” away from their original paths. However, random deflection routing may send packets to several different paths, thereby introducing packet re-ordering. This could affect the quality of receptions, it could also impair the overall performance in transporting data traffic. Nevertheless, the present study reveals that deflection routing could actually reduce delay-jitter when the traffic loading on the network is not heavy.     

不确定性自私路由模型的理论和应用

为了更加准确地描述现实生活中的交通情况,以经典的自私路由模型为基础,在边的费用函数上引入不确定性,从而定义了具有不确定性的自私路由模型.对于不确定性自私路由模型,采用三种费用衡量标准,风险厌恶型（保守型）、风险折衷型（理智型）、风险偏好型（乐观型）,分别对应着不同人群在现实中的选择.进而定义了在不同衡量标准下所形成的稳定策略,即纳什均衡策略,并且证明了在任何一种衡量标准下,纳什均衡策略总是存在并且本质是唯一的.接着对三种费用衡量标准下的纳什均衡费用进行了比较,发现了一种反直观的现象：风险厌恶型（保守型）衡量标准下的纳什均衡费用可能严格低于风险偏好型（乐观型）衡量标准下的纳什均衡费用,即有可能会出现高风险低回报,低风险高回报的情况,这与经济学中高风险高回报,低风险低回报的原则是相违背的.以此为基础,进而提出了一种自私路由风险性悖论,并证明了这种自私路由风险回报悖论本质上是传统布雷斯悖论的推广.最后,刻画出了不会发生自私路由风险回报悖论的网络结构,证明了一个单对始终点网络不会发生自私路由风险回报悖论当且仅当它是序列-平行网络.     

Asymptotic optimality of the Round–Robin policy in multipath routing with resequencing

We consider a model of a multipath routing system where arriving customers are routed to a set of identical, parallel, single server queues according to balancing policies operating without state information. After completion of service, customers are required to leave the system in their order of arrival, thus incurring an additional resequencing delay. We are interested in minimizing the end-to-end delay (including time at the resequencing buffer) experienced by arriving customers. To that end we establish the optimality of the Round–Robin routing assignment in two asymptotic regimes, namely heavy and light traffic: In heavy traffic, the Round–Robin customer assignment is shown to achieve the smallest (in the increasing convex stochastic ordering) end-to-end delay amongst all routing policies operating without queue state information. In light traffic, and for the special case of Poisson arrivals, we show that Round–Robin is again an optimal (in the strong stochastic ordering) routing policy. We illustrate the stochastic comparison results by several simulation examples. The work of the first author was supported through an ARCHIMEDES grant by the Greek Ministry of Education. The work of the second author was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government.     

Approximate dynamic programming with Bézier Curves/Surfaces for Top-percentile Traffic Routing

Multi-homing is used by Internet Service Providers (ISPs) to connect to the Internet via different network providers. This study develops a routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the θth highest volume of traffic shipped). We call this problem the Top-percentile Traffic Routing Problem (TpTRP).Solution approaches based on Stochastic Dynamic Programming require discretization in state space, which introduces a large number of state variables. This is known as the curse of dimensionality in state space. To overcome this, in previous work we have suggested to use approximate dynamic programming (ADP) to construct value function approximations, which allow us to work in continuous state space. The resulting ADP model provides well performing routing policies for medium sized instances of the TpTRP. In this work we extend the ADP model, by using Bézier Curves/Surfaces to obtain continuous-time approximations of the time-dependent ADP parameters. This modification reduces the number of regression parameters to estimate, and thus accelerates the efficiency of parameter training in the solution of the ADP model, which makes realistically sized TpTRP instances tractable. We argue that our routing strategy is near optimal by giving bounds.     

A stochastic and dynamic routing policy using branching processes with state dependent immigration

A stochastic and dynamic vehicle routing problem called the Dynamic Traveling Repairman Problem (DTRP) was introduced by Bertsimas and van Ryzin. Several routing policies were analyzed in light traffic and in heavy traffic conditions. But, the good light traffic policies become very quickly unstable with increasing traffic intensity, and the good heavy traffic policies are inefficient in light traffic conditions. In this paper, a new routing policy is defined and analyzed, using results from branching processes with state dependent immigration. This policy not only performs optimally in light traffic, but also performs very well in heavy traffic. This is important to the designer of a service system because the traffic conditions may be variable and/or be unpredictable, and having to switch routing policies could prove to be costly and difficult to implement.     

Multi-period traffic routing in satellite networks

We introduce a traffic routing problem over an extended planning horizon that appears in geosynchronous satellite networks. Unlike terrestrial (e.g., fiber optic) networks, routing on a satellite network is not transparent to the customers. As a result, a route change is associated with significant monetary penalties that are usually in the form of discounts (up to 40%) offered by the satellite provider to the customer that is affected. The notion of these rerouting penalties requires the network planners to explicitly consider these penalties in their routing decisions over multiple time periods and introduces novel challenges that have not been considered previously in the literature. We develop a branch-and-price-and-cut procedure to solve this problem and describe an algorithm for the associated pricing problem. Our computational work demonstrates that the use of a multi-period optimization procedure as opposed to a myopic period-by-period approach can result in cost reductions up to 13% depending on problem characteristics and network size considered. These cost reductions correspond to potential savings of several hundred million dollars for large satellite providers.     

On-line routing of random calls in networks

 We consider a random sequence of calls between nodes in a complete network with link capacities. Each call first tries the direct link. If that link is saturated, then the `first-fit dynamic alternative routing algorithm' sequentially selects up to d random two-link alternative routes, and assigns the call to the first route with spare capacity on each link, if there is such a route. The `balanced dynamic alternative routing algorithm' simultaneously selects d random two-link alternative routes; and the call is accepted on a route minimising the maximum of the loads on its two links, provided neither of these two links is saturated. We determine the capacities needed for these algorithms to route calls successfully, and find that the second `balanced' algorithm requires a much smaller capacity. Our results strengthen and extend the discrete-time results presented in [10]. Received: 10 January 2002 / Revised version: 7 July 2002 / Published online: 28 March 2003     

On a bi-dimensional dynamic alternative routing method

The analysis of a bi-dimensional dynamic routing model for alternative routing telecommunication networks led to the identification of an instability problem in the synchronous path selection associated with the complex interdependencies among the coefficients of the objective functions and the computed paths for every node pair. In this paper an analytical model enabling to make explicit this problem and evaluate its effects in terms of two global network criteria, is presented. Also a heuristic procedure dedicated to overcome this instability problem and select “good” compromise solutions in terms of network performance is developed. Finally the performance of the proposed routing method using the heuristic is compared by recurring to discrete-event simulation with a reference dynamic routing method (Real Time Network Routing) for some test networks.