Trunk Reservation Research Articles

Near-explicit state probabilities of multiservices loss systems

The Kaufman-Roberts (1981) multirate recurrence equation is converted to a functional equation subject to a single step parameter d, which defines the state-dependent recurrence depth of the multirate model. This parameter, d, is verified to be the joint solution of two moment-generating functions. In contrast to the multirate transform domain solution, the characteristic function of the functional model may be inverted explicitly. But this inverse is scaled by d and yields a new state-dependent probability density based on two types of scaled gamma functions. They uniformly cover wide areas of continuous states, capacities C, and demands. A two-moments series expansion of d in the transform domain signifies that it models the effective bitrate of the multirate connections under progress within a complete sharing mode of C. Selected case studies show very good agreements to the exact Kaufman-Roberts' state probabilities and to the high accurate Mitra-Morrison's (1994) tail probabilities. Further partial sharing mode investigations include an efficient approximation for connection admission controls by trunk reservation covering partial and full fairness. The resulting state and tail probabilities deviate only slightly from Roberts' approximations of the past. All solutions achieve time complexities of O(1) per state, which amount to O(SC) with iterative multirate recurrence solutions for S service classes.

Hierarchical virtual partitioning-algorithms for virtual private networking

This paper discusses the hierarchical virtual partitioning (HVP) concept, which facilitates the sharing of a resource, such as a link, by multiple customers, each having various service classes. Calls of each service class have distinctive bandwidth requirements, arrival rates, and mean holding times, and quality of service (QoS) is in terms of call blocking probabilities. The algorithms devised provide for the desired mix of fairness, robustness, and multiplexing efficiency at each of two levels — namely, at the customer level and at the level of the various services of each customer. The HVP scheme relies on nominal allocations of capacities to each customer and service, as well as priorities in the call admission process implemented by dynamic trunk reservations. The paper gives an approximate method of analysis based on fixed-point equations. In addition, a reward/penalty paradigm is devised to reflect the issues in virtual private networking, and the performance of our algorithms is compared to the optimal solution. The results show that the HVP scheme is fair, efficient, and robust.

Integrated model for performance analysis of multiple class-of-service Internet

A framework is developed for performance analysis of an integrated model of multiple class-of-service Internet. An Internet service provider is considered who provides premium, assured and best-effort services to end-users. Various aspects of the model are studied including link bandwidth allocation/sharing policies, user behaviours and service price-quality structure design. An analytic Markov model is developed and equilibrium performance measures are derived. Based on the analytical model, numerical analysis demonstrates the importance of trunk reservation in providing service protection and bandwidth sharing and the effects of user behaviours on service price and quality design. To get more insight on service price and quality design, two service quality declaration mechanisms are studied, i.e. static and dynamic service quality declarations under the assumption of static pricing. Simulation results show that the dynamic service quality declaration offers better performance when traffic level/pattern varies.

A dynamic call admission policy with precision QoS guarantee using stochastic control for mobile wireless networks

Call admission control is one of the key elements in ensuring the quality of service in mobile wireless networks. The traditional trunk reservation policy and its numerous variants give preferential treatment to the handoff calls over new arrivals by reserving a number of radio channels exclusively for handoffs. Such schemes, however, cannot adapt to changes in traffic pattern due to the static nature. This paper introduces a novel stable dynamic call admission control mechanism (SDCA), which can maximize the radio channel utilization subject to a predetermined bound on the call dropping probability. The novelties of the proposed mechanism are: (1) it is adaptive to wide range of system parameters and traffic conditions due to its dynamic nature; (2) the control is stable under overloading traffic conditions, thus can effectively deal with sudden traffic surges; (3) the admission policy is stochastic, thus spreading new arrivals evenly over a control period, and resulting in more effective and accurate control; and (4) the model takes into account the effects of limited channel capacity and time dependence on the call dropping probability, and the influences from nearest and next-nearest neighboring cells, which greatly improve the control precision. In addition, we introduce local control algorithms based on strictly local estimations of the needed traffic parameters, without requiring the status information exchange among different cells, which makes it very appealing in actual implementation. Most of the computational complexities lie in off-line precalculations, except for the nonlinear equation of the acceptance ratio, in which a coarse-grain numerical integration is shown to be sufficient for stochastic control. Extensive simulation results show that our scheme steadily satisfies the hard constraint on call dropping probability while maintaining a high channel throughput.

Performance analysis of alternate routing with trunk reservation in multirate switched networks

The traditional approach to implementing call routing in PSTN networks uses trunk reservation to achieve high throughput by avoiding possible routing oscillations in dynamic alternate routing. The purpose of trunk reservation in PSTN networks that support only a single class of traffic, e.g. voice is to limit the use of alternate paths for call routing when the network is heavily loaded. In this paper, we model the system of dynamic alternate routing with trunk reservation for multirate switched networks where the Markov chain is not time reversible, and analyze it by using an iteration method. Then as the calculation to find the optimal reservation size is intractable, we slightly modify the conventional Kaufman's recursive method that has been applied for the reversible Markov chain system. The complexity of the modified approximation is the same as that of the Kaufman's method. For a network of which link capacity is 50 channels, the approximation shows quite similar results to the analysis. For a network of which link capacity is 750 channels, which state size is not workable, we compare our approximation with simulation results. If we count some computation errors caused by the reduced load effect in the approximation, we can conclude that our approximation is quite accurate. As alternate routing with trunk reservation is expected to run on the top of multirate switched networks, our proposed approach can be used to obtain the near optimal trunk reservation size in real time, which results in maximal throughput.

A Refinement of the Hunt-Kurtz Theory of Large Loss Networks, with an Application to Virtual Partitioning

This paper gives a refinement of the results of Hunt and Kurtz on the dynamical behavior of large loss networks. We introduce a Liapounov function technique which, under the limiting regime of Kelly, enables the unique identification of limiting dynamics in many applications. This technique considerably simplifies much previous work in this area. We further apply it to the study of the dynamical behavior of large single-resource loss systems under virtual partitioning, or dynamic trunk reservation, controls. We identify limiting dynamics under the above regime, describing the behavior of the number of calls of each type in the system. We show that all trajectories of these dynamics converge to a single fixed point, which we identify. We also identify limiting stationary behavior, including call acceptance probabilities.

Two-Link Approximation Schemes for Loss Networks with Linear Structure and Trunk Reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.

Potential Interactions between IP-dial and Voice Traffic on the PSTN

This paper considers possible interactions that arise when IP-dial (i.e. Internet access via the PSTN) and voice traffic share the same infrastructure. The concern is caused by the different properties of the two traffic streams, with IP-dial being associated with long call hold times and automatic redialling. In order to gain an understanding, a simple single-link system is extensively studied using simulation. The results show that automatic redialling causes the IP-dial traffic stream to be much more efficient at seizing circuits than the voice traffic when the system is overloaded, and therefore congested. The use of various controls to establish a more equitable distribution of circuit resource between the two traffic streams in the event of congestion is considered and trunk reservation selected as the preferred control. Additional simulations establish appropriate trunk reservation settings and establish its efficacy. The paper concludes that network operators should consider carefully the effect of mixing IP-dial and voice traffic on shared infrastructure, and that trunk reservation is the preferred technique for controlling unwanted interactions.

Analysis of dynamic service separation with trunk reservation policy

The paper is concerned with the analysis of dynamic service separation under the trunk reservation policy. In the framework of dynamic service separation, statistical multiplexing of cell streams from each service can be well captured by an equivalent capacity that may take a nonlinear form. The conventional trunk reservation policy is extended to consider the nonlinear equivalent capacity. Various connection admission control schemes are formulated to implement blocking equalisation and blocking prioritisation regimes. In particular, the fixed, state-dependent, and hybrid trunk reservation schemes are proposed and compared with the complete sharing scenario. To solve the call-blocking probabilities, a simple yet efficient approximation procedure is carried out, based on an extension of the linear approximation model. Numerical results are reported on the effectiveness of the formulated blocking equalisation and blocking prioritisation regimes, and the degree of accuracy of the proposed approximation procedure.

Providing End-to-End Quality of Service with Optimal Least Weight Routing in Next-Generation Multiservice High-Speed Networks

Routing algorithms play a critical role in meeting both the stringent quality of service (QoS) requirements of guaranteed services and the certain QoS requirement of assured services over next-generation multiservice high-speed networks. In this paper, we propose the use of optimal least weight routing (OLWR) algorithm for routing QoS flows in high-speed networks. The main principle of our algorithm is that the choice of the most appropriate route is based on a set of parameters (least weight parameters) that estimate and consider the impact that the acceptance and routing decision of a call request belonging to a specific class would have on the network and other classes of service. Effective bandwidth, bandwidth and trunk reservation techniques, along with load balancing and packing trade-off considerations, are also introduced in the proposed routing algorithm. The performance evaluation of our algorithm is achieved via modeling and simulation of multiclass service routing in various network topologies. The performance results demonstrated that OLWR outperforms both the multihop least-loaded routing algorithms and the multihop most-loaded routing algorithms in terms of both revenue and carried load.

QoS-aware routing in ATM and IP-over-ATM

This paper analyzes the performance of some dynamic routing algorithms for ATM and IP-over-ATM networks. The main algorithm, named AR-DLCP (Alternate Routing — Distributed Least Congested Path), is based on a distributed computation, where the “best” route is chosen node-by-node in the call set-up phase, by taking decisions on the basis of a cost function, composed of a local part and an aggregate part. The local cost is constructed for each outgoing link on the basis of the knowledge of the current and the maximum number of connections that the link can support, while still ensuring the required Quality-of-Service at the cell level. The aggregate cost is aimed at reflecting the congestion situation of a node and is computed through an information exchange mechanism among adjacent nodes. In a fully connected core network, only direct and two-hop paths are considered; in the general meshed topology case, paths are organized in a two-level hierarchy. Static and dynamic trunk reservation schemes that guarantee enough bandwidth to direct paths are discussed. The performance of the two alternatives is evaluated by simulation under various traffic load situations. In particular, AR-DLCP is compared with other algorithms already in the literature as DLCP, Learning Automata and RTNR (Real Time Network Routing). In the general topology case, the algorithm is also combined with a bandwidth allocation mechanism and IP routing, by taking into account the presence of best-effort traffic, in an IP-over-ATM context.

Approximation for overflow moments of a multiservice link with trunk reservation

In this paper we propose an approximation for individual overflow moments of a multiservice link with differing arrival rates, capacity requirements and mean holding times, where trunk reservation is used. The approximation is a generalization of Roberts’ well-known approximation for individual blocking probabilities of a multiservice link to higher moments. It can be computed very efficiently. The quality of the approximation for the second moment (variance) is comparable to Roberts’ approximation for the individual blocking probabilities. Thus the results provide an efficient algorithm for computing the two moment characterization of the individual overflow streams and hence can be used for the design and analysis of circuit switched alternate routing networks with trunk reservation links.

On optimal call admission control in resource-sharing system

In this paper, we consider call admission control of multiple classes without waiting room. We use event-based dynamic programming for our model. We show that sometimes the customer classes can be ordered: if it is optimal to accept a class, then to accept a more profitable class is optimal too. We demonstrate submodularity of the minimum cost for the 2-classes problem and establish some properties of optimal policies. Then we formulate a fluid model that allows us to study the optimal control for the large-capacity case. We show that in the case of same service time distributions, the control problem can be reduced to a model with a one-dimensional (1-D) state space, and a trunk reservation policy is optimal. We present numerical examples that validate our results.

Traffic overflow in loss systems with selective trunk reservation

We consider two traffic streams competing for service at an n-server queuing system. Jobs from stream 1, the protected stream, are blocked only if all n servers are busy. Jobs from stream 2, the best effort stream, are blocked if n− r, r≥1, servers are busy. Blocked customers are diverted to a secondary group of c− n servers with, possibly, a different service rate. For the case r=1, we calculate the joint probabilities of the number of primary and secondary busy servers. For r>1, we describe a procedure for deriving the joint probabilities. These probabilities allow for the calculation of various performance measures including the overflow probabilities of the primary server and secondary server group. Our model is applicable to traffic control in communication networks that use the selective trunk reservation method.

An efficiency limit of cellular mobile systems

In order to limit handoff blocking probability, in cellular systems admission control can be applied to new call requests and resources reserved for future handoff attempts. Such resource reservation strategies have been widely studied in the literature. The denial of new call attempts, however, impacts system throughput creating a trade-off with handoff performance. The contribution of this paper is an analytical investigation of this trade-off. In particular, we study the impact of handoff on a cellular system's efficiency which we define as the system's throughput normalized by the theoretically optimal throughput at zero user mobility. As a reference case, we first determine the efficiency of a hypothetical system with deterministic advance reservation. Next, we consider systems with statistical reservation and calculate the maximum achievable efficiency, under the set of possible local admission control strategies subject to a hard constraint on the probability of call failure due to handoff blocking. Local admission control strategies are investigated because they represent efficient, yet simple strategies that lend themselves to easy implementation. We note that trunk reservation is a special case of local policies. We relate the calculated efficiency bound to call and mobility characteristics and show that the achievable efficiency decreases with decreasing cell size and with the increasing proportion of multimedia calls, both of which are recognized trends today.

Three management policies for a resource with partition constraints

Management of a bufferless resource is considered under non-homogeneous demand consisting of one-unit and two-unit requests. Two-unit requests can be served only by a given partition of the resource. Three simple admission policies are evaluated with regard to revenue generation. One policy involves no admission control and two policies involve trunk reservation. A limiting regime in which demand and capacity increase in proportion is considered. It is shown that each policy is asymptotically optimal for a certain range of parameters. Limiting dynamical behavior is obtained via a theory developed by Hunt and Kurtz. The results also point out the remarkable effect of partition constraints.

Three management policies for a resource with partition constraints

Management of a bufferless resource is considered under non-homogeneous demand consisting of one-unit and two-unit requests. Two-unit requests can be served only by a given partition of the resource. Three simple admission policies are evaluated with regard to revenue generation. One policy involves no admission control and two policies involve trunk reservation. A limiting regime in which demand and capacity increase in proportion is considered. It is shown that each policy is asymptotically optimal for a certain range of parameters. Limiting dynamical behavior is obtained via a theory developed by Hunt and Kurtz. The results also point out the remarkable effect of partition constraints.

BIAS OPTIMALITY IN A QUEUE WITH ADMISSION CONTROL

We consider a finite capacity queueing system in which each arriving customer offers a reward. A gatekeeper decides based on the reward offered and the space remaining whether each arriving customer should be accepted or rejected. The gatekeeper only receives the offered reward if the customer is accepted. A traditional objective function is to maximize the gain, that is, the long-run average reward. It is quite possible, however, to have several different gain optimal policies that behave quite differently. Bias and Blackwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies. This paper focuses on describing the structure of stationary, deterministic, optimal policies and extending this optimality to distinguish between multiple gain optimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among these gain optimal policies using the bias or transient reward and extend to Blackwell optimality.

Bounds and Policies for Dynamic Routing in Loss Networks

We consider the problem of maximizing a weighted sum of expected rewards in steady-state in multiclass loss networks under dynamic routing and admission control, with Poisson arrivals and exponentially distributed holding times. By aggregating the underlying Markov decision process, we derive linear programming relaxations that contain the achievable performance region under all admissible policies and lead to a series of progressively tighter upper bounds. These relaxations allow stronger bounds at the expense of higher computational times. We further propose a series of routing and admission control policies from the relaxations that outperform, in computational experiments, other heuristic policies, such as the dynamic alternative routing with trunk reservation and the least busy alternative routing, variations of which are used in practice. The suboptimality guarantees defined as best bound/best policy range from 0 to 2.5% under symmetry conditions (symmetric network topology, arrival rates, link capacities, rewards), and from 4% to 10% under asymmetry conditions. We discuss the qualitative behavior of these policies and obtain insights about their performance.

A linear-based trunk reservation routing algorithm for ATM networks

In this paper a practical routing algorithm is proposed that increases the network throughput irrespective of the network traffic load. Its effectiveness is based on an efficient cost function which achieves a successful trade-off between the use of the minimum-hop routes and the application of the load-balancing concept. Moreover, it employs the known Trunk Reservation notion according to a probability that increases linearly with the traffic load. This results in an effective compromise of the performance of the algorithm between light and heavy traffic loads. Finally, its simplicity and its suitability for a real-time application render it as an efficient routing algorithm for ATM networks. Copyright © 1999 John Wiley & Sons, Ltd.