The evolutionary penetration of the satellite services and demand in the telecommunication market during the last decades has created the need for decision making tools for a satellite operator [1] [2] . There is still an incremental growth to the telecommunication applications and services [3] [4] . A number of studies have proposed methodologies and tools for the techno-economic evaluation of different aspects of satellite communication dealing with physical, operational, design performance and risk parameters [5] . The need for in-depth analysis of the economic feasibility of new telecommunication solutions that take into account both technological and econometric characteristics of the applications, has become obvious, both in industrial and academic community. This study deals with the creation and assessment of an optimal business policy of a Satellite Operator. The ability of real time decisions has a significant effect to the viability and profitability of the company in the growing and competitive satellite market. The decision making model presented here is an applied tool for assessment purposes, which deals with real problems and can be used as such, by any Satellite Operator. Limited work has addressed the revenue modeling [6] in terms of market penetration, expected profits and risks, in order to provide a quantitative estimation to the Satellite Operator (after the launching) for the optimal business decision making.

The problem of determining the optimal leasing policy for satellite services, at different time periods is similar to an inventory control problem, with evolution in time, incorporating dynamic and stochastic elements [7] [8] , modified accordingly to address the specific application [9] . The purpose of our work is to model and quantify this problem, using heuristic techniques, as well as to evaluate the outcome. The validation of this work results from its usage by the Greek Satellite Operator in the last five years and the development of a new methodology based on stochastic dynamic optimization, presented in [10] with similar results.

We present a model that compares different scenarios of combinations of customers asking to hire satellite capacity. There is a variety of services that a satellite can support. For each of these services requested by a customer, there is a different bandwidth demand, duration of lease, and a different price. The purpose of this work is to find the most profitable case for the incumbent operator. Each scenario leads to a decision tree. This maximization problem is described in terms of real and expected revenues, along with the corresponding probability of getting them. The final outcome leads to optimal enterprise steps that maximize revenues and enable the evaluation of different contingency plans. The decisions are taken successively in a time horizon and thus the presented tool incorporates time evolution. Consequently the model is dynamic.

At the first stage of the work, demand and pricing data have been gathered from the international market. These data provided by the operating Satellite firm i) are statistically processed to produce mean values and standard deviations for each service and each bandwidth demand when needed, and ii) are integrated into a mathematical model, implemented at the second stage, and taking into account all possible states and stages [11] . The model evaluates all probable revenues, along with their associated risks that could result from each alternative decision branch. The concept of the tool gives the benefit of accessing alternative courses of action, to the decision maker. Depending on the company policy at each time period, variant enterprise steps could be followed. Sensitivity analysis is included, in order to determine the impact of small errors in parameters estimates to the final decision. It is performed using both mathematical calculation of the shadow prices and heuristic calculation, providing consistent results.

The paper is organized as follows: Sections 2 and 3 describe the stages of work followed and the main concept of the model. Section 4 formulates the mathematical model and Section 5 presents the sensitivity analysis of the proposed model.

The first stage of this study involves the recording and the evaluation of the pricing data coming from the international market of leasing satellite capacity as well as their statistical processing. Some charging schemes have been proposed for broadband networks while this work involves real pricing data [12] . A decision making tool that maximizes the profits of a satellite operator, is implemented in the second stage. The goal of the proposed model is to enable the decision maker, to determine the best possible scenario for the satellite operator, which is the scenario with the larger amount of income.

The hypothesis that a satellite operator has different lease demands from different customers is made. Each customer wants to hire satellite capacity with a specified bandwidth, for a given lease period, which has an associated cost. The model output provides guidelines on the combination of customers that is the most profitable for the operator.

A scenario can be customized by entering the characteristics of the customers. These are:

: the type of the requested service,

: the ascending number of customer

(MHz): the capacity in MHz that the -th costumer requires. If the required capacity is more than 36 MHz, then it can occupy one or more transponders completely. Therefore, for our calculations instead of we compute, which is the remaining capacity that does not occupy a whole transponder:

: the starting time (month) for which the k-th customer requires the leasing of capacity, considering a horizon of five years,

: the ending time (month) for which the k-th customer requires the leasing of capacity, , and

: the corresponding cost of lease, in Euros, for the k-th customer depending on the type of the requested service.

In the structure of the model, the possibility of beginning the hire in different time periods (different months) is included. Table 1 shows an example of the input parameters of the model.

The indicative cost for each service, is calculated using the data collected from the global satellite market. From the gathered data we created a basic classification of the possible services that a satellite operator could offer. These services correspond to different bandwidth demands and are presented in Table 2. The statistical analysis includes the pricing for the equivalent capacity, per 36 MHz, per month and the duration of lease in months. For each service, the mean value, the standard deviation, and the percentage of difference between standard deviation and mean value of these measures are determined along with their cross-correlation. Similar quantities are calculated for the duration of hire.

The underlying concept of the problem of optimal allocation of the available satellite spectrum is based on a heuristic approach of the inventory control problem [7] . In the context of the proposed work, the model enables the comparison of 10 at most possible incoming customers with maximum required lease duration of 60 months, corresponding to a typical level of satellite demand. However, the model can easily be expanded to compare more customers requiring satellite capacity, for more than 5 years.

All the possible combinations of customers are calculated (see Figure 1 Group A), where a description of these combinations is given in terms of feasibility to implement or not. Specifically, there is an indication of Possible, Not Possible or Negotiable Combination for each combination of customers.

A Negotiable Combination is the combination of customers that exceeds by 1 MHz at most the highest possible capacity that a transponder can serve i.e. 36 MHz, which can probably constitute an issue of negotiation between the provider and the consumer. A Possible Combination is the feasible combination of customers from the point of view of the maximum capacity of the transponder and a Not Possible Combination is a not feasible one. The proposed tool gives the benefit of sorting by the Description of combination in order to present all the Possible Combinations (see Figure 1 Group B). The next step is to extract the Possible Combinations that are best to compare, by examining the most promising ones. This is done by selecting the combinations with the highest amount of total occupied capacity, which is the sum of the requested capacity by each customer of the combination (see Figure 1 Group C). Obviously, the more bandwidth is occupied from a transponder, the more profit there will be for the firm. These are the “Real Revenues”. This confines the search for the best case scenario to a small number of possible combinations.

The next step is to decide which of these combinations, with high occupied capacity, are more profitable. The criteria that are used to lead to the optimum combination are:

a) the amount of Real Revenues, representing the revenues that an operator will gain from hiring the capacity to the customers of each combination,

b) the calculation of Additional Expected Future Profits for the satellite operator, taking into consideration the standard deviation of the prices and consequently the corresponding risk.

Each combination has different time of maximum requested capacity hire. Therefore, in order to properly compare different scenarios, it is necessary to reduce them to the same time period i.e. to the same month of maximum hiring. We include to our calculations the additional possible income that can be acquired by this left over-free capacity that is called the “Remaining Capacity” (C Remaining). It is also possible that at specific months, not all the available capacity of the transponder of the satellite will be occupied with each combination. This leads to the undesirable effect of not having maximum occupancy of the transponder of the satellite, at each month. So the satellite operator could probably hire out this available capacity, to other possible future customers that are not included in the combination, and gain more revenues. This is called the “Empty Capacity” (C Empty). These moreover profits, consist the Additional Expected Future Profits.

Let us examine the following example involving two cases that a satellite operator may need to compare and decide which one leads to maximum revenues. These are Scenario 1, which includes the combination of the customer number 1, 2, 3, 4 and 5 (Figure 2) and Scenario 2, which includes the combination of the customer number 6, 7, 8, 9 and 10 (Figure 3), with the characteristics shown in Table 1.

The sum of the occupied capacity of the transponder by the customers of the combinations in Scenario 1 and Scenario 2 are shown in Figure 4 and Figure 5, respectively. These figures represent the profile of the satellite transponder occupancy.

In Scenario 1, the maximum demand on the transponder’s capacity occurs during the 22nd month, while in Scenario 2, it occurs during the 30th month. The additional possible income that can be acquired from this left over free capacity is calculated. This is the “Remaining Capacity” (C Remaining) and appears at the white region in Figure 4.

Each Scenario does not lead to maximum occupancy of the transponder of the satellite at each month. This “Empty Capacity” (C Empty) is shown as the lined region of Figure 4 and Figure 5. For instance, in Scenario 1 (Figure 4) there are 21 MHz of unoccupied capacity during the 1st month, 20 MHz during the 2nd month, 5 MHz from the 3rd to the 5th month, 0 MHz between the 5th and the 10th month, etc. These expected profits are included to our calculations.

Figure 6 shows the general structure of the model. This was implemented in Microsoft. NET environment in order to meet the need for increased computational burden. All feasible combinations of objects per, are

, with. All feasible combinations of 10 customers per 10, starting from 2 customers per 2 and more, are. It is meaningless to include cal-

culations with only one customer, since this will not result to maximization of the profits for the operator.

The tool starts with the input as shown in Table 1, which is the demand of the customers that arrives to the satellite operator. Then all the combinations of customers are being calculated taking into account the evolution in time. The possible revenues for each scenario resulting from the leasing of the Remaining and the Empty Capacity are computed, using demand and pricing Parameters.

Sensitivity analysis is necessary in validating the efficiency of a model. Due to the stochastic nature of the input parameters, we calculate the variance to the output of the model, caused by small variation of the input. The statistical processing of the pricing data gathered from the international market provided us with pricing and probability parameters. Since these variables may not be very accurate, we study the effect caused by small errors on their values.

These parameters include three categories:

Ÿ pricing and demand (probability) data concerning the Remaining Capacity categorized on each type of service,

Ÿ pricing and demand (probability) data concerning the Empty Capacity categorized on each selected range of capacity and

Ÿ the Probability of a new incoming customer asking the Satellite provider for satellite services.

The sensitivity analysis for these input parameters was performed by creating a small perturbation for each one of them. The value of each parameter was varied by ±2% and the corresponding change in the output, which is the Total Expected Revenues (TER), was measured. The analysis was performed in two different ways: first by theoretical calculation of the shadow prices of the input parameters and second using a heuristic technique, implemented by immediate application of the input-change to the model and observation of the output.

In this paper, we consider the techno-economic valuation of satellite services. The incremental growth of the satellite market nowadays, makes important the study of the economic feasibility of a satellite operator considering technological aspects of the application.

A dynamic mathematical model addressing the decision needs of an operator that provides satellite services is created. This decision making tool considers different demands of customers that arrive to the satellite operator.

Demand and pricing data have been gathered and statistically processed, from the international market. We present a model that compares different scenarios of combinations of customers with different demands, asking to hire satellite capacity. The model evaluates all probable revenues, along with their associated risks that could result from each decision branch. The tool incorporates all the valuable information that will help the satellite operator to determine the most profitable leasing scenario and allows alternative courses of enterprising steps depending on the company policy.

Sensitivity analysis has been included and showed a very small impact of the uncertainty of the input demand and pricing parameters to the final decision. This analysis could also be extended on simultaneous changes of several combinations of input parameters. This work addresses the real need of optimal satellite business planning. Other analysis was mainly referred to the economic evaluation to the physical layer of satellite planning.

The benefits of the model and of the analysis presented here for any satellite operator are clear. The same benefits may apply to related areas of activity where leasing of specific volumes to customers is the essence of the business enterprise.

Finally, we are currently extending our work, using the dynamic programming formulation, in discrete time and with stochastic elements.

This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)-Research Funding Program: THALES, Investing in knowledge society through the European Social Fund. The authors would also like to express their appreciation to Hellas Sat [13] , the Greek Satellite Operator, for their valuable support in data providing, developed tool usage and validation through business practice.