Optimal Incentive Pricing on Relaying Services for Maximizing Connection Availability in Multihop Cellular Networks

Table 1

Comparison between the fixed-rate pricing scheme, the location-based pricing scheme, and the proposed pricing scheme of Example 4.3.

	Fixed-rate pricing scheme	Location-based pricing scheme	Proposed pricing scheme
Incentive price on relaying services	𝑝1=𝑝3=𝑝6=𝑝7=𝑝8=𝑝10=; 0.5𝑃max	𝑝1=0.625𝑃max	𝑝1=0.8763𝑃max
		𝑝6=0.567𝑃max	𝑝3=0.7474𝑃max
		𝑝3=𝑝7=𝑝10=0.45𝑃max	𝑝6=𝑝7=𝑝8=0
		𝑝8=0.1𝑃max	𝑝10=𝑃max
Connection availability of each; node	CA2=CA3=𝑆(𝑝1)=0.5	CA2=CA3=𝑆(𝑝1)=0.625	CA2=CA3=𝑆(𝑝1)=0.8763
	CA4=CA5=𝑆(𝑝1)𝑆(𝑝3)=; 0.25	CA4=CA5=𝑆(𝑝1)𝑆(𝑝3)=; 0.281	CA4=CA5=𝑆(𝑝1)𝑆(𝑝3)=0.6549
	CA7=𝑆(𝑝6)=0.5	CA7=𝑆(𝑝6)=0.567	CA7=𝑆(𝑝6)=0
	CA8=𝑆(𝑝6)𝑆(𝑝7)=0.25	CA8=𝑆(𝑝6)𝑆(𝑝7)=0.255	CA8=𝑆(𝑝6)𝑆(𝑝7)=0
	CA9=𝑆(𝑝6)𝑆(𝑝7)𝑆(𝑝8)=; 0.125	CA9=𝑆(𝑝6)𝑆(𝑝7)𝑆(𝑝8)=; 0.026	CA9=𝑆(𝑝6)𝑆(𝑝7)𝑆(𝑝8)=0
	CA11=CA12=𝑆(𝑝10)=0.5	CA11=CA12=𝑆(𝑝10)=0.45	CA11=CA12=𝑆(𝑝10)=1
Connection availability of the networks	(0.5+0.5+0.25+0.25+0.5+0.25+0.125+0.5+0.5)/9=0.375	(0.625+0.625+0.281+0.281+0.567+0.255+0.026+0.45+0.45)/9=0.3956	(0.8763+0.8763+0.6549+0.6549+0+0+0+1+1)/9=0.5625
Relaying costs	2𝑢(0.5𝑃max)+2𝑢(0.5𝑃max+0.5𝑃max)+𝑢(0.5𝑃max)+𝑢(0.5𝑃max+0.5𝑃max)+𝑢(0.5𝑃max+0.5𝑃max+0.5𝑃max)+2𝑢(0.5𝑃max)=7𝑢𝑃max	2𝑢(0.625𝑃max)+2𝑢(0.625𝑃max+0.45𝑃max)+𝑢(0.567𝑃max)+𝑢(0.45𝑃max+0.567𝑃max)+𝑢(0.1𝑃max+0.45𝑃max+0.567𝑃max)+2𝑢(0.45𝑃max)=7.001𝑢𝑃max	2𝑢(0.8763𝑃max)+2𝑢(0.8763𝑃max+0.7474𝑃max)+2𝑢(𝑃max)=7𝑢𝑃max