chapter 4

6/20/ 2002 EMIS 8392 Maya Petkova 1

Chapter 4Chapter 4

Traffic and Cost Traffic and Cost Generators – Cost Generators – Cost GeneratorsGenerators


OverviewOverview

• In most networks – the single largest expense In most networks – the single largest expense item is the cost of the bandwidth.item is the cost of the bandwidth.

• Routers with purchase cost of Routers with purchase cost of $10,000(amortized cost $300/month) can $10,000(amortized cost $300/month) can terminate links that cost $20,000/month.terminate links that cost $20,000/month.

• Besides the TRAFFIC table The TARIFF table Besides the TRAFFIC table The TARIFF table represents the largest data structure needed to represents the largest data structure needed to pose a network problem.pose a network problem.


Types of TariffsTypes of Tariffs

• Tariff is a published rate for Tariff is a published rate for telecommunications services and facilities (in telecommunications services and facilities (in U.S. carriers file tariffs with FCC).U.S. carriers file tariffs with FCC).

• 2 types of links : 2 types of links :

- usage-insensitive or leased- usage-insensitive or leased

- usage-sensitive - usage-sensitive • In telephony most individual links are usage-In telephony most individual links are usage-

sensitive.sensitive.


Types of Tariffs – Usage Types of Tariffs – Usage Sensitive Voice TariffsSensitive Voice Tariffs

• A simple usage-sensitive voice tariff:A simple usage-sensitive voice tariff:

• Fixed cost for the use of line.Fixed cost for the use of line.• Can place outgoing calls for an additional fee.Can place outgoing calls for an additional fee.• Unlimited incoming calls (the calling party pays).Unlimited incoming calls (the calling party pays).• The tariff is specified in 1-minute increments.The tariff is specified in 1-minute increments.


Types of tariffs – Usage-Types of tariffs – Usage-insensitive Voice Tariffsinsensitive Voice Tariffs

• Usage-insensitive tariffs come in variety of Usage-insensitive tariffs come in variety of types based on the locations involved.types based on the locations involved.

• Suppose we have a call center located 200 Suppose we have a call center located 200 miles from a large cit, Anagon, where we have miles from a large cit, Anagon, where we have several hundred customers.several hundred customers.


Types of tariffs – Usage Types of tariffs – Usage

insensitive Voice Tariffs – Cont’dinsensitive Voice Tariffs – Cont’d

• Leased line – need a tandem voice switch in Leased line – need a tandem voice switch in Anagon that can connect the leased line with a Anagon that can connect the leased line with a trunk in the local phone system.trunk in the local phone system.

• Out-of-district line gives a line that appears to Out-of-district line gives a line that appears to be in Anagon. Reduces the per-minute charge be in Anagon. Reduces the per-minute charge for outgoing calls from $0.095 per minute to for outgoing calls from $0.095 per minute to $0.03 per minute.$0.03 per minute.

• Banded WATS (wide area telephone service) (4 Banded WATS (wide area telephone service) (4 hours/day) – allows up to 4 hours of calls per hours/day) – allows up to 4 hours of calls per day to locations that are no more than a day to locations that are no more than a certain specified distance, for instance 250 certain specified distance, for instance 250 miles. miles.


Types of tariffs – Usage-Types of tariffs – Usage-insensitive Voice Tariffs – Cont’dinsensitive Voice Tariffs – Cont’d

• Banded WATS with unlimited usage within the Banded WATS with unlimited usage within the same 250 mile circle.same 250 mile circle.

• Nationwide WATS - national coverage with Nationwide WATS - national coverage with unlimited usage.unlimited usage.

• Banded WATS are more expensive.Banded WATS are more expensive.


Types of tariffs – Usage-Types of tariffs – Usage- sensitive Data Tariffs sensitive Data Tariffs

• X.25 and ISDN are deployed in parts of the world.X.25 and ISDN are deployed in parts of the world.• Users can place a data call much as they would place a Users can place a data call much as they would place a

voice call .voice call .• Users will be charged a fixed cost + a cost/minute.Users will be charged a fixed cost + a cost/minute.• Optionally users are charged a cost/bit or a cost/packet.Optionally users are charged a cost/bit or a cost/packet.• In other parts of the world data one demand is limited to In other parts of the world data one demand is limited to

modems operating over voice-grade lines. modems operating over voice-grade lines.


Types of tariffs – Usage-Types of tariffs – Usage-insensitive Data Tariffsinsensitive Data Tariffs

• Limited to speeds consistent with the multiplexing Limited to speeds consistent with the multiplexing hierarchy for the country.hierarchy for the country.

• In U.S. rates are 56 Kbps; fractional T1, e.g. 128 Kbps, In U.S. rates are 56 Kbps; fractional T1, e.g. 128 Kbps, 192 Kbps, 256 Kbps, 384 Kbps, 512 Kbps, 768 Kbps; and 192 Kbps, 256 Kbps, 384 Kbps, 512 Kbps, 768 Kbps; and full T1.full T1.

• In Europe there is normally only multiples of 64 Kbps, In Europe there is normally only multiples of 64 Kbps, including half E1 = 1024 Kbps.including half E1 = 1024 Kbps.

• Usage-insensitive data tariff for U.K.Usage-insensitive data tariff for U.K.


Tariff TaxonomiesTariff Taxonomies

Given the number of ways of buying bandwidth Given the number of ways of buying bandwidth and connectivity and the number of ways of and connectivity and the number of ways of paying for it, we need a taxonomy of link costs paying for it, we need a taxonomy of link costs - that is to make a decision how to categorize - that is to make a decision how to categorize all the types of links into a relatively small set all the types of links into a relatively small set of examples. of examples.

Note: No taxonomy is complete. Note: No taxonomy is complete.


Tariff Taxonomies – Link Tariff Taxonomies – Link TypesTypes – Fixed Virtual Circuits – Fixed Virtual Circuits

• Leased links that can be filled with voice calls Leased links that can be filled with voice calls or data at any hour of the day or night.or data at any hour of the day or night.

• They are usually in place for months or years.They are usually in place for months or years.• Have substantial installation costs, in order of 1 Have substantial installation costs, in order of 1

or 2 months rent.or 2 months rent.• Often derived from higher-speed links by TDMOften derived from higher-speed links by TDM• Clocked to the network – different form the Clocked to the network – different form the

situation in asynchronous modems where users situation in asynchronous modems where users transmit whenever they like.transmit whenever they like.


Tariff Taxonomies – Link Tariff Taxonomies – Link TypesTypes – Dialed Virtual Circuits – Dialed Virtual Circuits

• Can be set up or torn down on demand.Can be set up or torn down on demand.• Often not available at the same speed as fixed Often not available at the same speed as fixed

virtual circuits. Example: a T3 link at 45 Mbps virtual circuits. Example: a T3 link at 45 Mbps is only available as a fixed virtual circuit, not as is only available as a fixed virtual circuit, not as dialed virtual circuit.dialed virtual circuit.

• Conventional phone uses dialed virtual circuits.Conventional phone uses dialed virtual circuits.


Tariff Taxonomies – Link Tariff Taxonomies – Link TypesTypes – Fixed Pipes – Fixed Pipes

• Define Define pipepipe to be a communication link that accepts bits to be a communication link that accepts bits at a certain rate and makes an effort (the supplier at a certain rate and makes an effort (the supplier usually calls it a best effort) to deliver the bits to the usually calls it a best effort) to deliver the bits to the other end. Examples – X.25, frame relay, and SMDS other end. Examples – X.25, frame relay, and SMDS (switched multimegabit data service).(switched multimegabit data service).

• Many pipes can share the same physical interfaceMany pipes can share the same physical interface• Note: with virtual circuit the data rate and the circuit Note: with virtual circuit the data rate and the circuit

rate are the same, in pipes they can be quite different. rate are the same, in pipes they can be quite different. Suppose we have frame relay connection with 64 Kbps Suppose we have frame relay connection with 64 Kbps peak rate and a 16 Kbps CIR ( committed information peak rate and a 16 Kbps CIR ( committed information rate). We are only guaranteed to use the link to an rate). We are only guaranteed to use the link to an average of 0.25 of its capacity. average of 0.25 of its capacity.


Tariff Taxonomies – Link Tariff Taxonomies – Link Types Types – Dialed Pipes – Dialed Pipes

• Pipes that can be set up or torn down upon Pipes that can be set up or torn down upon demand.demand.

• Have the same service characteristics as the Have the same service characteristics as the fixed pipes.fixed pipes.

• Charging structure is usage sensitive.Charging structure is usage sensitive.


Tariff Taxonomies – Link Tariff Taxonomies – Link Types – Cont’d Types – Cont’d

Along with the previously described link taxonomy we Along with the previously described link taxonomy we have a list of possible fees:have a list of possible fees:

1. Access fees ( the cost of maintaining a physical 1. Access fees ( the cost of maintaining a physical network connection).network connection).

2. Setup fees. 2. Setup fees. 3. Teardown fees.3. Teardown fees. 4. Usage fees, which depend on4. Usage fees, which depend on - channel capacity- channel capacity - CIR- CIR - distance- distance - time of day- time of day - national and administrative borders- national and administrative borders


Tariff Taxonomies – RelationshipTariff Taxonomies – Relationship to the Network Design Process to the Network Design Process

Q1. How to obtain and organize all the Q1. How to obtain and organize all the informationinformation

mentioned so far in a reasonable way so that mentioned so far in a reasonable way so that it it

can be made use of in the design process?can be made use of in the design process?

Q2. How do we automate the process so that Q2. How do we automate the process so that

gathering the tariff data doesn’t become the gathering the tariff data doesn’t become the

largest part of the design process?largest part of the design process?


Distance-Based CostingDistance-Based Costing

• Calculating link costs is not very simple.Calculating link costs is not very simple.• Sometimes costs can be very odd.Sometimes costs can be very odd.• The tariff world represents anomalies like those The tariff world represents anomalies like those

found in airline tariffs.found in airline tariffs.• Example: NY-LA cheaper air fares than NY-Example: NY-LA cheaper air fares than NY-

Montreal because of the competition.Montreal because of the competition.• Link from NY- Montreal can be more expensive Link from NY- Montreal can be more expensive

than a link from NY to LA. Competition serves than a link from NY to LA. Competition serves to depress the market if there is excess to depress the market if there is excess capacity. Crossing national borders plays role capacity. Crossing national borders plays role in decreasing competition.in decreasing competition.


Linear Distance-BasedLinear Distance-Based Costing Costing

Cost models for fixed virtual circuits and fixed Cost models for fixed virtual circuits and fixed pipes: generating the monthly rental cost.pipes: generating the monthly rental cost.

• Cost of a circuit between 2 sites that are km Cost of a circuit between 2 sites that are km apart is apart is

- fixed cost- fixed cost - variable cost- variable cost• A D64 virtual circuit might have a fixed cost of A D64 virtual circuit might have a fixed cost of

$1200 and a variable cost $2.50/km. A circuit $1200 and a variable cost $2.50/km. A circuit of 200 km will cost $1700/month.of 200 km will cost $1700/month.

• Unfortunately most tariffs differ significantly Unfortunately most tariffs differ significantly from this simple modelfrom this simple model


Linear Distance-Based Linear Distance-Based Costing – Cont’d Costing – Cont’d

• Interesting use of liner distance-based costing Interesting use of liner distance-based costing is to estimate tariffs when the exact tariff is is to estimate tariffs when the exact tariff is known but is unreasonably complex.known but is unreasonably complex.

• Tariff may be published as a gigantic table. Tariff may be published as a gigantic table. There may be 400 cities in a country, and the There may be 400 cities in a country, and the tariff for a D64 line is published as a table of tariff for a D64 line is published as a table of length .length .

The table is published on paper. If we do not The table is published on paper. If we do not want to scan 100 pages and convert into ASCII want to scan 100 pages and convert into ASCII via OCR (optical character recognition) we can via OCR (optical character recognition) we can take a number of city pairs from the table and take a number of city pairs from the table and fit into a linear distance-based tariff.fit into a linear distance-based tariff.


Linear Distance-BasedLinear Distance-Based Costing – Cont’d Costing – Cont’d

• Represent the data as: Represent the data as:

where where • Do a least square fit of the data to a linear Do a least square fit of the data to a linear

functionfunction• Minimize Minimize • Min occurs when the partial derivatives are 0. Min occurs when the partial derivatives are 0.


Linear Distance-BasedLinear Distance-Based Costing – Cont’d Costing – Cont’d

• Solve in terms of and .Solve in terms of and .• It will work quite well in certain limited cases – if It will work quite well in certain limited cases – if

all the cites are within a country or within the all the cites are within a country or within the service region of a company within a country, the service region of a company within a country, the tariff might be exact.tariff might be exact.

• Example: In U.K. we can use the approximation ofExample: In U.K. we can use the approximation of

$757.09 + $2.40/km$757.09 + $2.40/km

for the cost of a 128 Kbps circuit. In the U.S. the for the cost of a 128 Kbps circuit. In the U.S. the circuit between central offices would becircuit between central offices would be

$605.00 +$0.49/mile$605.00 +$0.49/mile


Piecewise-Linear Distance-Piecewise-Linear Distance- Based Costing Based Costing

• Definition 4.2.Definition 4.2. A piecewise-linear function A piecewise-linear function on on

with breaks at is continuous on with breaks at is continuous on and is linear on the intervals and is linear on the intervals

• Many tariffs are published in piecewise-linear Many tariffs are published in piecewise-linear format.format.

• Cost per mile or km is in bands. Cost per mile or km is in bands.


Piecewise-Linear Piecewise-Linear Distance-Distance- Based Costing – Cont’d Based Costing – Cont’d

Piecewise-linear tariff for a T1 circuit between Piecewise-linear tariff for a T1 circuit between central offices in the U.S. and Mexico.central offices in the U.S. and Mexico.

Piecewise linear tariff for 56 Kbps link between Piecewise linear tariff for 56 Kbps link between U.S. and Canada.U.S. and Canada.


Piecewise-ConstantPiecewise-Constant Distance-Based Costing Distance-Based Costing

• Another model for costs is a step function.Another model for costs is a step function.• Japanese tariff for a D64 line.Japanese tariff for a D64 line.


Tariff NirvanaTariff Nirvana

Even if the data is available finding the Even if the data is available finding the charges can be tricky.charges can be tricky.

Q. What would be the ideal solution to the tariff Q. What would be the ideal solution to the tariff problem?problem?

A.A. Tariff library or a tariff client/server interface Tariff library or a tariff client/server interface that allowed us to ask for tariffs on demand that allowed us to ask for tariffs on demand so we could write the following code:so we could write the following code:

PNODE newyork, paris;PNODE newyork, paris; cost = tariff_nirvana(newyork, paris, cost = tariff_nirvana(newyork, paris, ““T1T1””, ,

““ANYCARRIERANYCARRIER””, , ““FIBERFIBER” ); ” ); aand get magically nd get magically the the correctcorrect result result


Tariff Nirvana – Cont’dTariff Nirvana – Cont’d

We are long way from tariff nirvana:We are long way from tariff nirvana:

- often tariffs do not exist- often tariffs do not exist

- while it is easy to get a tariff from Dallas to - while it is easy to get a tariff from Dallas to London, it can be another thing to get a tariff London, it can be another thing to get a tariff from Caracas, Venezuela to Beijing, Chinafrom Caracas, Venezuela to Beijing, China

- if there are no direct circuits between 2 - if there are no direct circuits between 2 countries, there is probably no filed tariffcountries, there is probably no filed tariff

- the tariffs is not just a function of the 2 - the tariffs is not just a function of the 2 endpoints; it also depends on the country endpoints; it also depends on the country where the service is bookedwhere the service is booked



• Not clear which is the correct tariff to use.Not clear which is the correct tariff to use.• Good example: U.S. and Canada – circuits Good example: U.S. and Canada – circuits

between these countries are treated differently between these countries are treated differently from other international circuits and differently from other international circuits and differently from national circuits.There is a question on from national circuits.There is a question on optimizing the link cost across multiple optimizing the link cost across multiple carriers. carriers.

• Another good tariff example: in U.S. with the Another good tariff example: in U.S. with the notion of LATA (local access and transport notion of LATA (local access and transport area) – the cost of a circuit between 2 sites in area) – the cost of a circuit between 2 sites in different LATA uses a different tariff than would different LATA uses a different tariff than would be used if both points are in the same LATA.be used if both points are in the same LATA.



• Tariffs are misleading – could appear that tariff Tariffs are misleading – could appear that tariff offers low rate between 2 sites but when go to offers low rate between 2 sites but when go to provision the circuit we may find that the there provision the circuit we may find that the there are no facilities or the lead time to provide the are no facilities or the lead time to provide the circuit is unacceptably long.circuit is unacceptably long.

• There are parts of the world where the cost of a There are parts of the world where the cost of a simple phone is not prohibitive, but the wait for simple phone is not prohibitive, but the wait for a phone is measured in decades. a phone is measured in decades.

• If a network is large enough there are If a network is large enough there are negotiated tariffs that allow carrier to have a negotiated tariffs that allow carrier to have a special deal with a customer. special deal with a customer.


Tariff ToolsTariff Tools

• Network designers and network operators are the Network designers and network operators are the single largest group of customers of businesses single largest group of customers of businesses that produce tariff tools and tariff references. that produce tariff tools and tariff references.

• Companies in the tariff tool business:Companies in the tariff tool business: - NAC Corp. - PRICER tool produces tariffed costs - NAC Corp. - PRICER tool produces tariffed costs

in North America. Extensions of this tool cover in North America. Extensions of this tool cover most of the first worldmost of the first world

- LYNX - LYNXGTD tool is very comprehensive, - LYNX - LYNXGTD tool is very comprehensive, strong on pricing international circuits, weaker on strong on pricing international circuits, weaker on prices within countriesprices within countries

- Tarrifica – they produce a tariff book, relatively - Tarrifica – they produce a tariff book, relatively comprehensivecomprehensive


A Sequence of Cost A Sequence of Cost Generators Generators

• Commercial tariff tools are expensive.Commercial tariff tools are expensive.• 5 different cost generators that can generate 5 different cost generators that can generate

costs for sample problems or for real work are costs for sample problems or for real work are describeddescribed

• Interesting problems can be developed with Interesting problems can be developed with piecewise-linear tariffs.piecewise-linear tariffs.

• Cost Generator 1 and Cost Generator2 – for Cost Generator 1 and Cost Generator2 – for academic studies, the other 3 for those who are academic studies, the other 3 for those who are trying to do actual design work.trying to do actual design work.

• Costgen.cCostgen.c – source code with – source code with DELITEDELITE• COSTALGCOSTALG will control which generator to be used will control which generator to be used


Cost Generator 1Cost Generator 1

• Inputs: Inputs:

- SITES table with locations in V&H or L&L- SITES table with locations in V&H or L&L

- TARIFF-UNIVERSAL table as shown below- TARIFF-UNIVERSAL table as shown below

• Output: matrix of size where is the Output: matrix of size where is the number of sites and is the number of link number of sites and is the number of link types defined in the TARIFF-UNIVERSAL table.types defined in the TARIFF-UNIVERSAL table.


Cost Generator 1 – Cont’dCost Generator 1 – Cont’d

• The algorithm passes through all node pairs. Fixed cost The algorithm passes through all node pairs. Fixed cost is is abbreviated as and the cost/km as is is abbreviated as and the cost/km as

If distance form to is thenIf distance form to is then

• Requires min amount of info to produce cost tableRequires min amount of info to produce cost table• It will do well within a LATA in U.S. or within a country It will do well within a LATA in U.S. or within a country

with a simple charging structure like U.K.with a simple charging structure like U.K.• Can not produce realistic tariffs covering sites in several Can not produce realistic tariffs covering sites in several

countries – too simple.countries – too simple.• Best way of generating tariffs for test problems with min Best way of generating tariffs for test problems with min

amount of manual workamount of manual work



• Inputs: Inputs:


- TARIFF-UNIVERSAL table as shown below with - TARIFF-UNIVERSAL table as shown below with 2 additional fields2 additional fields

• Output: matrix of size where is the Output: matrix of size where is the number of sites and is the number of link number of sites and is the number of link types defined in the TARIFF-UNIVERSAL table.types defined in the TARIFF-UNIVERSAL table.



• Extends our linear model to a piecewise-linear.Extends our linear model to a piecewise-linear.

• Not realistic for international tariffs.Not realistic for international tariffs.



• The costs of services in the U.S. and Mexico are quite The costs of services in the U.S. and Mexico are quite different as are the costs of services in Germany and different as are the costs of services in Germany and France. We can deal with it by overlaying the output of France. We can deal with it by overlaying the output of the Cost Generator 2 with the country specific the Cost Generator 2 with the country specific information.information.

• Inputs: Inputs:


- TARIFF-UNIVERSAL table as shown below- TARIFF-UNIVERSAL table as shown below



• TARIFF-NAT table as shown belowTARIFF-NAT table as shown below


Cost Generator 3 – Cont’dCost Generator 3 – Cont’d• Output: matrix of size where is the number Output: matrix of size where is the number

of sites and is the number of link types defined in the of sites and is the number of link types defined in the TARIFF-UNIVERSAL table.TARIFF-UNIVERSAL table.

• is first filled with values from the TARIFF-is first filled with values from the TARIFF-UNIVERSAL table using piecewise-linear cost generator. UNIVERSAL table using piecewise-linear cost generator. After that is done, a second pass through the sites is After that is done, a second pass through the sites is taken. If the country code for site and are both taken. If the country code for site and are both country , then we recalculate the tariff for the node country , then we recalculate the tariff for the node pair pair

• Strong relationship between the economy of scale offered Strong relationship between the economy of scale offered by the tariff and the shape of the final networkby the tariff and the shape of the final network



• Approximate international circuit pricing.Approximate international circuit pricing.• Many large companies have located facilities Many large companies have located facilities

throughout the world. We need whole range of throughout the world. We need whole range of international tariffs. They can be supplied on a international tariffs. They can be supplied on a country-pair vs. node-pair basis.country-pair vs. node-pair basis.

• International costs are usually sum of 2 pieces International costs are usually sum of 2 pieces referred to as half-circuits.referred to as half-circuits.

• For most country pairs (A,B) the cost of circuit For most country pairs (A,B) the cost of circuit from anywhere in country A to anywhere in from anywhere in country A to anywhere in country B is the same.country B is the same.



• Inputs: Inputs:

- SITES table - SITES table

- TARIFF-UNIVERSAL table- TARIFF-UNIVERSAL table

- TARIFF-NAT table- TARIFF-NAT table

- TARIFF-HCKT table as shown below with additional columns to - TARIFF-HCKT table as shown below with additional columns to clarify the country codeclarify the country code


Cost Generator 4 – Cost Generator 4 – Cont’dCont’d

• Output: matrix of size where is the number Output: matrix of size where is the number of sites and is the number of link types defined in the of sites and is the number of link types defined in the TARIFF-UNIVERSAL table.TARIFF-UNIVERSAL table.

• is first filled with values from the TARIFF-is first filled with values from the TARIFF-UNIVERSAL table using piecewise-linear cost generator. UNIVERSAL table using piecewise-linear cost generator. Then we use the TARIFF-NAT table to overwrite values for Then we use the TARIFF-NAT table to overwrite values for sites within a country. If site is in and site is in sites within a country. If site is in and site is in

then we recalculate the tariff for the node pairthen we recalculate the tariff for the node pair

if both half-circuits are presentif both half-circuits are present



• Allows us to specify some overrides and Allows us to specify some overrides and investigate special tariffs available between investigate special tariffs available between some city pairssome city pairs

• Inputs: Inputs:

- SITES table - SITES table

- TARIFF-UNIVERSAL table- TARIFF-UNIVERSAL table

- TARIFF-NAT table- TARIFF-NAT table

- TARIFF-HCKT- TARIFF-HCKT

- TARIFF-OVERRIDE table as shown on slide 42- TARIFF-OVERRIDE table as shown on slide 42



After all of the tariffs are computed using the After all of the tariffs are computed using the TARIFF-UNIVERSAL table, the TARIFF-NAT table, TARIFF-UNIVERSAL table, the TARIFF-NAT table, the TARIFF-HCKT table as a final step we read the TARIFF-HCKT table as a final step we read through TARIFF-OVERRIDE table and replace through TARIFF-OVERRIDE table and replace the individual entries of with costs in the individual entries of with costs in the this table.the this table.


SummarySummary

• Traffic and cost generation allows us to take Traffic and cost generation allows us to take the SITES table of entries and produce the the SITES table of entries and produce the TRAFFIC and TARIFF tables which have TRAFFIC and TARIFF tables which have entries.entries.

• If these tables were produced manually they If these tables were produced manually they would take up most of our time which could be would take up most of our time which could be used to create good designs.used to create good designs.

• Traffic and cost generators are packaged into a Traffic and cost generators are packaged into a single program called network generator which single program called network generator which allows us to pose a complete design problem. allows us to pose a complete design problem.

chapter 4

Documents

unlimited usage

voice calls

types of links

maya petkova tariff

maya petkova overviewin

fixed cost

variety of types

amortized cost