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This paper presents a dynamic mathematical model of optimal leasing allocation of satellite band-width and services in terms of expected revenues and associated risk. This tool meets the need of a Satellite Operator to determine the optimal leasing policy of the available bandwidth. A methodology and a tool for techno-economic evaluation of satellite services are developed. The output of the tool enables the policy decisions to be customized by the attitude toward risk that the company wants to apply at each time period. The study is based on inputs concerning data and services from an existing Satellite Operator and addresses a real situation. Demand and pricing data have been gathered from the international market. The decision making tool is given in the set-up of a decision tree presenting quantified alternative leasing policies and risks. Sensitivity analysis is also performed to measure the efficiency of the model.

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 [

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 [

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 [

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 [

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:

In the structure of the model, the possibility of beginning the hire in different time periods (different months) is included.

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

K | ||||||
---|---|---|---|---|---|---|

1 | A | 1 | 15 | 15 | 12 | 15 |

2 | B | 3 | 10 | 8 | 15 | 20 |

3 | C | 2 | 20 | 19 | 1 | 1 |

4 | D | 6 | 22 | 17 | 5 | 10 |

5 | E | 1 | 16 | 16 | 3 | 5 |

6 | F | 1 | 18 | 18 | 5 | 5 |

7 | G | 3 | 10 | 8 | 18 | 30 |

8 | H | 11 | 15 | 5 | 19 | 20 |

9 | I | 4 | 30 | 27 | 8 | 9 |

10 | J | 3 | 23 | 21 | 4 | 3 |

s | Services |
---|---|

1 | VSAT |

2 | Telephony |

3 | IP Gateway |

4 | Corporate |

5 | Broadcast |

6 | Video Contribution |

7 | Media company |

8 | Government |

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 [

All the possible combinations of customers are calculated (see

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

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 (

The sum of the occupied capacity of the transponder by the customers of the combinations in Scenario 1 and Scenario 2 are shown in

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

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

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

All the possible combinations of the customers (PCf),

where

For our calculations we specify the following intermediate parameters:

_{k}

We assign

For each scenario the possible revenues from the future leasing of the “Empty Capacity” up to the 36 MHz, are calculated.

The Empty Capacity

where

This calculation is categorized depending on the amount of bandwidth that is not used each month by the customers of each combination. This “Empty Capacity” could potentially be hired out and generate revenues. The selected ranges of capacity in MHz are shown in

We are considering

to a capacity

We use the notation:

The selected capacity ranges along with the corresponding probability of appearance of a new incoming customer, have been statistically computed by the available gathered data (

A decision tree arises for each scenario, as shown in

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

1.3 | 4 | 6 | 10 | 18 | 33 | 36 |

The Expected Values of theoretical income, resulting from the “Empty Capacity” for each combination, depending on the not-leased bandwidth at each time period, are calculated as:

The standard deviation of the Expected Value, for each combination is:

The probable revenues for each combination, which are called Theoretical Revenues, depending on the number of MHz that are not used, are calculated as:

While the standard deviation of the Theoretical Revenues for each combination is:

The Expected Values of Revenues are calculated as intermediate volumes, which are used only for comparison purposes among scenarios. Such revenues incorporate the corresponding risk, and measure the monetary value of each scenario. The values of Theoretical Revenues are the real amounts of money (in Euros) that can be acquired, following each branch of the decision tree.

We proceed analogously calculating all possible revenues, (Expected Values and Theoretical Revenues) that can result from the leasing of the “Remaining Capacity”. This calculation is categorized depending on the type of service (s), using the statistically processed data (

First, we calculate the remaining time

maximum requested month of lease by the customers of the (PCf) combination, until the max requested time of all compared scenarios.

The following variables are introduced:

These variables also constitute the Parameter data set and have been statistically calculated by the available gathered data.

The Expected Values of theoretical income for the Remaining Capacity depending on the type of service are:

The standard deviation of the Expected Value for each combination is:

While the Theoretical Revenues for the Remaining Capacity are:

and the standard deviation of the Theoretical Revenues for each combination is:

All the calculations concerning demand as well as the mean values of the prices of lease and standard deviations of prices are based on statistical computation of the real data coming from the international market and constitute the Parameter data set.

All of these evaluated data are presented in the form of a unified decision tree (

The amount of Total Expected Revenues that will estimate the optimal policy for the firm is the sum of all revenues. This sum consists of the Real Revenues, plus the Expected Value resulting from the leasing of the Empty Capacity, plus the Expected Value resulting from the leasing of the Remaining Capacity, including their standard deviations, which are the Additional Expected Future Profits.

The Real Revenues are:

where

the satellite operator, and belongs to the Input Parameters. An indicative cost, for each service, which applies to the international market, has been calculated by the gathered data. These values provide information to the incumbent operator for the current trends of satellite services billing and can be modified accordingly.

The Total Expected Revenues give a range of values, defining the best and worst case scenario for the revenues of the satellite operator.

where:

and

The real amount of money, resulting from each brand of the decision tree that will possibly result to the satellite operator is:

where:

and

This gives the opportunity to the satellite provider to determine which combination is the most profitable, for the present and in the future. The decision is made using the amount of Total Expected Revenues. This is not the real revenue that can be acquired, but it is an intermediate amount, which takes into account the corresponding probabilities, and is used for comparison purposes of the scenarios. The Total Expected Revenues is a decision quantity that incorporates profits and associated risk. This amount gives an estimate of the extent/worthness of the risk.

The decision making process starts from the identification of the highest Real Revenues, then the possible additional revenues are considered with their corresponding standard deviation that measures risk. This result to a

range of Total Expected Revenues with central value:

The final decision depends on the extent of risk that the firm is willing to take and on the particular policy that wants to apply. For a risk-loving decision maker the policy generating the highest Total Expected Revenues (upper limit) is chosen. A risk-neutral decision maker will take the policy with the central value, whereas for a risk-averse decision maker the policy generating the lowest of Total Expected Revenues (lower limit) will be chosen. The real amount of income that will result from each decision is the amount of Total Revenues of the corresponding scenario.

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:

pricing and demand (probability) data concerning the Remaining Capacity

pricing and demand (probability) data concerning the Empty Capacity

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.

The shadow prices of the price parameters

parameter that we would like to examine.

The Sensitivity of the Total Expected Revenues with respect to the parameter

The Sensitivity of the Total Expected Revenues with respect to the parameter

We proceed calculating the Bode Sensitivity function for the demand parameters

ing probabilities parameter, expressing the variation

The Sensitivity of the Total Expected Revenues with respect to the parameter

The Sensitivity of the Total Expected Revenues with respect to the parameter

The Sensitivity of the Total Expected Revenues with respect to the parameter

All parameters ranges, involved in the calculation of the sensitivity analysis are presented in

The Sensitivity analysis is now performed by immediate application of the variance of each input parameter, by ±2%, to the input of the model, and measuring of the output. A case study of six incoming customers, arriving to the satellite operator has been evaluated.

Two cases were considered. The best case scenario, which is the scenario generating the larger amount of expected revenues. This was identified by choosing for the calculations of the Remaining Capacity those that result from the Media Company Service, since it is the one with the highest pricing. The second case considered was the worst case scenario. This case accordingly resulted from the choice of Broadcast Service for the calculations of the expected revenues of the Remaining Capacity, which is the one with the lowest pricing. For each of these cases the calculations were extended to considering the upper limit and the lower limit of the Total Expected Revenues. A sensitivity analysis was performed for these 4 cases.

Using this small variation for each of the input parameters and for each case, we calculated 20 points of the output of the decision model, corresponding to different percentages of change of the input parameters between the ranges of ±2% of the central value.

For each change of input, the change of the output was calculated. This change has the form of the percentage of difference of the value of the output calculated for each of the 20 points of change to the input, minus the value of the output at the central point (11th point, with zero alteration), normalized to this central value.

Variable | |||||
---|---|---|---|---|---|

min | 0.62 | 0.0164 | 0.015 | 4.148 | 125.100 |

max | 0.270 | 0.277 | 6.114 | 295.834 |

min | 0.06% | 0.02% | 0.0002% | 0.0001% | 0.0089% |

max | 16.63% | 45.28% | 0.09% | 0.02% | 0.16% |

The results of the sensitivity analysis for the best case scenario are shown in Figures 11-14. For each of the 20 different input sets we calculated the output on the four most profitable combinations of customers. Scenario1, is the scenario with the higher amount of Total Expected Revenues, Scenario 2 is the one with the second higher amount of Total Expected Revenues and so on.

In Scenario 2 (

customers are zero.

The calculations were made for all 46 input parameters, categorized as shown in

The analysis showed very low sensitivity of the output to changes in the input parameters, even to the pricing parameters. The outcome using Heuristic calculations for the Sensitivity analysis were consistent with the outcome from the mathematical calculations. A small change to the pricing and to the demand parameters will not significantly change the output of the model. This is a very desirable feature, resulting from the good balancing of the proposed model. Even if the parameter data are not very accurate, the decision will not be greatly affected.

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 [