System Architecture

5.2.1 The Users Bid

The bids of the users is formulated as explained in section 4.2.2 and shown below:

ܾ௜(ܲݎܷ݅ܿ݁݊݅ݐ)=(ேೆ ೄಲ_ேିே_ಲ಴ಲ಴)௏೔+ ܸ௠ ௜௡ܨ݋ݎ݅= 1,2,3 … … . ܰ௎ௌ஺ (5.1)

In some part of this chapter, it is assumed that the users can estimate the value of the reserve price based on information provided by the broker unlike in chapter 4. Therefore, it is assumed that such users generate a bid above the reserve price as shown in equation (5.2)

Chapter 5 Energy Efficient dynamic Spectrum Auction Process with Utility function

124 Abdulkarim A. Oloyede, PhD Thesis, Department of Electronics, University of York.

(This does not increase the user’s budget). Hence, if a user possesses such information the user uses equation 5.2 as shown below rather than 5.1 to generate the offered bid value:

ܾ௜=(ேೆ ೄಲ_ேିேಲ಴)௏೔

ಲ಴ + ݎ୉ୱ୲ܨ݋ݎ݅= 1,2,3 … … . ܰ௎ௌ஺. (5.2) Whereݎாௌ் is the estimated value of the reserve price. The above assumption is formulated

in order to examine the effects of making the reserve price either known to the users or privately known to the auctioneer only. The equations were derived from conventional economics theory as explained in chapter 4.

5.2.2 The Reserve Price

The reserve price_{ݎis the minimum acceptable bid by the broker as shown below:}

ݎ௜(݌ݎܷ݅ܿ݁݊݅ݐ)=ܥ௙்ܰ஼ܥݎ (5.3)

ܥ௙ is the congestion factor,ܥ௥ is a constant in price units and ்ܰ஼ is the total number of

channels in the system both used and unused as explained in chapter 4.

ܥ௙ =ே_ேೆ ೄಲ_ಲ಴ (5.4)

5.2.3 Green Payments and Congestion Charge

The green payment concept is as explained and defined in chapter 4. It is as shown below:

R(Price Unit) = ቊ 2ଵାßఏ− 1ܨ݋ݎ݃ݎ݁݁݊݌ܽݕ݉ ݁݊ݐݏݑܾݏ݅݀ݕ

2ଵାßఏ_{+ 1ܨ݋ݎ݃ݎ݁݁݊݌ܽݕ݉ ݁݊ݐݐܽݔ}
(5.5)

Where the green payment factor (_{ß) is a constant and it was determined from chapter 4 and} ߠ is the absolute value of the linear difference between the SNR value for user ݅and the value of a set threshold represented as the _݆௧௛ SNR value as shown in equation (5.6) below. The parameters are exactly as explained in chapter 4.

ߠ௜= |ψ௜− ψ௝| for ݅=1, 2, 4…ܰ௎ௌ஺ (5.6)

|݆| = ⌊௉೎ேೆ ೄಲ

ଵ଴଴ +

ଵ

ଶ⌋ (5.7)

ܲ௖ is the desired percentile. It can be of any value between 0 and 100 (0≤ ܲ௖≤ 100). The

SNR of_ܰ௎ௌ஺arriving users can be arranged in ascending order as shown below:

ૐ௧= [ψଵ, ψଶ, ψଷ… ψேೆ ೄಲ] (5.8)

The HPU users are further charged a congestion charge which increases as the traffic load increases as shown in equation (5.9). The aim of the congestion charge is to use price to regulate the amount of congestion in the system and to increase the value of the tax paid as the traffic load increases as shown below. Furthermore in the modelling scenarios, a situation where the final bid value of any user remains positive after the deduction of green tax and the congestion charge is only examined. It is important to highlight here that the only changes made in this model so far compared to the model in chapter 4 is the introduction of _ݎ୉ୱ୲in equation 5.2 and_{ܮ in equation 5.9 below:}

ܾ_௜௙௜௡௔௟(݌ݎܷ݅ܿ݁݊݅ݐ) = ൝ܾܾ௜௜− ܮܴ+ ܴ௜௜

ܨ݋ݎLPU

ܨ݋ݎܪܷܲ (5.9)

For_{݅= 1, 2, 3….ܰ௎ௌ஺}

Where _{ܮ is the traffic load in Erlang, ܾ௙௜௡௔௟}and _ܴ௜is the final value of the bid in price unit and the green payment for user݅respectively after the deduction or addition of the congestion and green tax, _ψ௜஼ represents the SNR of user _{݅and the superscripts ܥ can either be ܮܷܲ or} ܪܷܲ. After the tax (green tax and congestion charge) and subsidy is applied as shown in equation (5.9), the highest_ܰ஺஼bidders are afterwards allocated a channel.

Chapter 5 Energy Efficient dynamic Spectrum Auction Process with Utility function

126 Abdulkarim A. Oloyede, PhD Thesis, Department of Electronics, University of York.

5.2.4 Energy Model and Energy Consumption Calculation

To measure and compare the energy consumed by the users in the system, a definition of measuring the user throughput compared to the energy consumed and the traffic load in the system as defined in chapter 4 is proposed. The transmission rate is a function of the SNIR of the user. The dependence of SNIR on the transmission rate used in this chapter is as given by the TSB as defined in chapter 3. This is similar to the model in [108].

5.2.5 Probability of a User Being Among the Highest_ࡺ࡭࡯Bidders (_ࡼ࢘ࡺ

࡭࡯) The probability (_ܲ௥ே

ಲ಴) is introduced in this chapter to prevent users who have a low probability of winning from attempting to transmit. Using the probability helps in reducing the number of users who attempt to transmit and eventually lose the auction process thereby wasting energy in the process. The scheme prevents such users from going into the transmission mode (ON) unnecessarily. The ON/OFF mode is as explained in section 3.8.2. The probability is dependent on the bid submitted by a user and the number of available channels in the system as shown below:

ܲ_௥ேಲ಴(݅) = ( ௕೔ି௕ೝ

௏೘ ೌೣି௕ೝ)

ேೆ ೄಲିேಲ಴_,ܰ_௎ௌ஺>ܰ_{஺஼ (5.10)}

Where _ܾ௥ can be the value of the reserve price if known to the user otherwise it is the minimum possible bid by user _{݅based on the user’s budget. ܸ௠ ௔௫} is the maximum possible valuation for a user. The probability is calculated for all the users intending to transmit during any bidding period. If the value of the probability is greater than or equal to a set probability threshold_{ܲ௥೅೓ೝ೐ೞ೓೚೗೏} (_ܲ௥ே

ಲ಴(݅) ≥ ܲ௥೅೓ೝ೐ೞ೓೚೗೏) the user is allowed to attempt otherwise the user stays out of the process. This is further explained in section 5.3.

5.2.6 Blocking

In this chapter, two types of blocking are considered. Blocking that occurs because of price and blocking due to insufficient transmission resources.

Blocking due to insufficient resources (_ܤூோ): A user(s) is blocked due to insufficient

resources when the SNIR is below the SNIR threshold or due to non-availability of transmission channel. This is the same as the blocking probability defined in chapter 3. This is calculated and shown as a fraction to differentiate it from the blocking due to price. Where ܰி஺ோ(ݐ) represents the number of failed transmission trials due to insufficient resources up to

time_{ݐand ܰ௧௥}represents the total number of trials up to time_ݐ

ܤூோ =ே_ேಷಲೃ_೟ೝ(௧)(௧) (5.11)

Blocking due to price (_ܤ௉): A user is blocked due to price if the bid is below the reserve

price or because of the _ܲ௥ே

ಲ಴is below the threshold. If any of the users are blocked due to price, then the number of users transmitting after the auction and allocation process _ܰ௎் is less than the number of available channels (_ܰ஺஼) or the number or winning bidders (_{ܰௐ ௎).} That is (_{ܰ௎்< ܰ஺஼݋ݎܰௐ ௎}). It is calculated as shown below in percentage in this chapter. Whereܰி஺௉represents the total number of failed trials due to price up to time t.

ܤ௉(%) =_ேே_೟ೝಷಲು_(௧) (5.12)