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In this paper we develop a novel method of controlling the demand in a multi-class, QoS-enabled network, using pricing and resource allocation for income maximisation. We first present a solution to the problem of calculating the optimal prices and QoS for a single link using a limiting regime approximation, which reduces the associated computational burden. A heuristic algorithm is then proposed that improves the limiting regime solution, achieving better results for links with small capacity. We further extend this approach to a multi-link network, where a distributed iterative algorithm is developed based on the solution of the single link model. Results from small and medium size networks show that, even when the assumptions we used do not hold, our approach yields results very close to the optimal ones (0.17–2.95% difference), which are computed by exhaustively searching in the decision space. Moreover, the calculation time using the proposed approach is approximately 1.5 min for problems which took more than 240 min to solve using exhaustive search.

In this paper we propose an approach to managing a telecommunication network by controlling the demand for services. In contrast to most existing approaches, which allow demand to depend either on prices or on quality, we examine the case where demand for a particular service depends on both these characteristics. We use this approach to solve the problem of maximising the income of a multi-class network provider using pricing and resource allocation. In the scenario here investigated the network provider is allowed to offer a limited selection of alternative classes of service to users. Each potential user, according to his/her price and quality requirements, will select the most appropriate and request a connection. Calls belonging to a specific class of service have identical characteristics. Our model is similar to the differentiated services model [30] in that: (i) there is a limited number of classes, (ii) packets or flows of packets of the same class are treated in the same way, and (iii) state information is proportional to the number of classes rather than the number of flows. In diffserv the classes’ quality of service (QoS) differs in terms of delay, jitter, reliability and other parameters. Using a value similar to effective bandwidth, our model may be a good approximation of the diffserv model. The exact mapping of other QoS requirements to bandwidth can be the subject of further research. We also note that, by making decisions for sets of calls (classes) rather than individual calls, the number of decisions to be made is greatly reduced, improving the scalability of our solutions. The tradeoff is that the decisions are not necessarily optimal for each individual user, since not all the users belonging to a class are characterised by identical requirements. We assume that, for a given price, an increase in the resources allocated for each call of a specific class leads to an increase of the QoS for this class. If this is the case, the number of potential users willing to subscribe to this class increases, since more users will find the offered quality acceptable. However, the extra resources which will now be used by the users which were already satisfied with the lower quality could have been used for other potential users which, even after the increase of QoS, are not satisfied with it. The unsatisfied users do not request connection and hence are lost from the system. For this reason, a proportion of the resources can be considered not optimally used. The exact amount of resources which are not optimally used in this sense, is the difference between the minimum resources needed to satisfy the total active users, and the actual resources used by them. It could be argued that these resources improve the utility of the users, and therefore may be considered optimally used, but from an income maximisation point of view, these resources do not contribute directly to the income of the network provider. In this paper we develop methods for minimising the amount of resources not used optimally, as defined earlier. These methods depend on pricing, since the willingness to pay is here considered as being related to the quality expected by a user. Setting different prices for each service is a method for ensuring that users do not request admission for a service which offers much better QoS than they need, assuming that users of low requirements are willing to pay a lower price, and in this way it partially alleviates the problem of misused resources mentioned earlier. Therefore, the way price and QoS are determined for each class greatly affects the efficiency of a network. We firstly explore the problem of finding optimal prices and qualities for the case of a single link, with the aim of maximising the income. We present a solution which is based on limiting regime approximation and then propose methods to improve this solution. We then develop a distributed iterative solution for the problem of a multi-link network, a solution which is based on the single link solution. 1.1. Related work Most published research uses pricing to control or regulate one of two things: either (i) the incoming rate of new connection requests or (ii) the data rate sent by existing connections or users. In this paper we use pricing to control the incoming rate of new connections. A method considering pricing for multiservice networks is presented in [10]. The QoS of each service is given and guaranteed, and the problem of pricing is formulated as an expected income optimisation problem. In contrast, in this paper, we take into account QoS as a decision variable, which affects demand when determining the optimal prices. Dynamic pricing policies for network services have also been widely investigated, and there is a great variety of propositions. Agent based [11], time-of-day [6], usage-based [29], threshold-based [20] and [7] and congestion-dependent pricing [19] and [12] are some of them. The work of Paschalidis et al. [16] and [17] on dynamic, congestion-dependent pricing suggests that static (congestion-independent) pricing is asymptotically optimal, and therefore the benefits from dynamic pricing may not worth the extra complexity especially for large networks with many calls. A distributed mechanism for resource allocation, based on the pricing results of [16] and [17] is given in [18]. In contrast to the above approaches, our model allows the provider to make only static decisions. Regarding static pricing, in the “Paris Metro Pricing” (PMP) scheme [15] and [21] two classes of services exist in the network, and each one has its own queue. Calls of the high class cost more than calls of the low class. In this way, fewer users request calls of the high class, and each call of the high class can thus use more resources, therefore receiving higher QoS. The PMP scheme exploits also the dependence of demand on prices. In this paper we extend the scheme proposed in PMP, as we also control and guarantee QoS. Another study based on demand and pricing, is the work of McKie-Mason and Varian [13], which assumes that users pay a price depending on the congestion of the network and the utilisation, which in turn depend on the demand curve of individual users and the price. In contrast, in the approach presented in this paper we focus on pricing and QoS for classes of service, rather than individual users, and in our model pricing is not congestion-dependent. Resource allocation using auction based pricing is another popular subject of research [25] and [26]. Compared to such studies, our approach is different in that the network provider informs the users about available prices and qualities and users can decide whether they will request a connection or not. Other researchers have addressed this problem resorting to a game-theoretic framework [14], [1], [28] and [27]. In such papers the users are considered players who compete against each other for resources, who adapt their demand (either by changing their rate or their priority/service class) to prices until an equilibrium is reached. This approach is not relevant in the scenarios studied in this paper were the provider sets and guarantees the quality and the price of each class, and each user just has to evaluate whether a class is satisfactory for him or not. In the work presented in [2] and [3], the authors study the performance of the network under different bandwidth partitioning policies. It is observed via simulations that the prices and QoS offered have an effect to the income of a network provider. In [6] the combined problems of provisioning and pricing are studied. By provisioning the authors mean the procedure by which the provider purchases bandwidth, which then is divided between two classes. Time of day pricing is used, and making decisions in different timescales is evaluated. Provisioning is based on the actual cost of bandwidth which is assumed to be purchased by the provider. In our work we assume that the provider owns the resources or has purchased them in advance, and therefore provisioning is done under the constraint of limited bandwidth. When addressing the problems of resource allocation and pricing for telecommunication networks, our approach brings revenue management ideas from operations research. Revenue management [4] aims at maximizing income through the application of tactics that predict customer behaviour and the optimisation of services availability and price. Revenue management has been successfully applied in industries like hotels or airlines, and it has been suggested that it can be applied in computer networks too [8]. We advocate that the service quality (QoS) is also a parameter which has to be considered in the case of telecommunication services. The operation of a network provider is a complex affair where several targets have to be met simultaneously. In our work we concentrate on the target of income maximisation, which, due to the fact that the marginal costs of a network provider are minimal, can be translated to profit maximisation. Any telecommunications business will need to assess their income as part of their operations viability and hence we investigate this aspect here. Other targets, which have been suggested in the research community are: (i) Welfare maximisation: ∑ui∑ui (The sum of all utilities of all users), and (ii) Fairness: maxminui ([24]). We note that the target of welfare maximisation can be achieved within the framework presented in this paper, where instead of price we consider the utility of the user. The underlying aim of this paper is to develop a suitable framework to manage the offering of classes of service (CoS) assuming that the demand for a particular CoS depends on prices and QoS. We propose a framework for the calculation of the optimal static decisions regarding prices and QoS. In Section 2 we describe how demand is modelled and its dependency to prices and quality. Then, the solution of the optimisation problem for a single link is presented in Section 3. Two solutions are developed; one based on a limiting regime approximation, and one based on a heuristic, that improves the limiting regime solution in the cases where the scale of the problem is small. Section 4 analyses the extension of the solution to a network of many links, developing a distributed solution. The paper ends with our conclusions and further research directions.

In this paper we analysed the problem of resource allocation and pricing, with the aim of income maximisation. The role of prices in a telecommunications environment can be twofold. Apart from being the well-known reward mechanism for the provider of the telecommunications resources, it is also a mechanism of selection and classification of users according to their utility requirements. The fact that users who demand higher services are prepared to pay more, can be used by the provider in any task that requires (or would be more efficiently performed with) segmentation or categorisation of the users. The problem we have addressed in this paper attempts to aid the decisions of a network provider regarding the quality and the price of calls belonging to different classes. After analysing the problem and its parameters, an approximation was presented, for the case when the number of calls of the route is very large. This approximation simplified all equations to a great extent. We developed a numerical method for improving the LR solution of [33], which would be more relevant for access links of smaller capacity. For the case of a network of many links, under the assumptions of link independence and similar load across different links, we have found an approximate solution which is within 3% from the optimal for all the cases studied, even when the assumption of uniform distribution, or the assumption of balanced load does not hold. For the approximate decentralised solution we use the Erlang fixed point iteration method. A matter of further research is to compare our algorithm to more general existing global optimisation methods. Another relevant extension of our work is to conduct a sensitivity analysis of our solution to the relationship between q and p. We are currently considering only static decisions in our model, but dynamic/adaptive versions of the algorithms presented in our paper are currently under investigation, where prices and quality change depending on the state of the network, and potential users are informed of the offered services and their prices. In general, although adaptive solutions offer better results in terms of income, this improvement comes at a cost, since the complexity of the decisions is increased, and users also face a more complicated system, where they cannot be sure about the prices in advance. Especially for the case of dynamic adjustments of prices and quality, preliminary results show that it is possible to improve the income from a network, but the complexity of the problem increases significantly. Another direction of research, which is currently under investigation, is balancing the relative load among alternative routes using pricing. This would improve the accuracy of our algorithm, which, as we show, partially relies on the assumption that the relative load is similar on all links.