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

Table 2

Comparison between the location-based pricing scheme and the proposed pricing scheme with QoS requirements of Example 4.3.

	Location-based pricing scheme	Proposed pricing scheme with QoS requirements
Incentive price on relaying services	𝑝1=0.625𝑃max	𝑝1=0.6539𝑃max
	𝑝6=0.567𝑃max	𝑝3=0.3085𝑃max
	𝑝3=𝑝7=𝑝10=0.45𝑃max	𝑝6=0.3165𝑃max
	𝑝8=0.1𝑃max	𝑝7=0.2313𝑃max
		𝑝8=0.3550𝑃max
		𝑝10=𝑃max
Connection availability of each node	CA2=CA3=𝑆(𝑝1)=0.625	CA2=CA3=𝑆(𝑝1)=0.6539
	CA4=CA5=𝑆(𝑝1)𝑆(𝑝3)=0.281	CA4=CA5=𝑆(𝑝1)𝑆(𝑝3)=0.2017
	CA7=𝑆(𝑝6)=0.567	CA7=𝑆(𝑝6)=0.3165
	CA8=𝑆(𝑝6)𝑆(𝑝7)=0.255	CA8=𝑆(𝑝6)𝑆(𝑝7)=0.0732
	CA9=𝑆(𝑝6)𝑆(𝑝7)𝑆(𝑝8)=0.026	CA9=𝑆(𝑝6)𝑆(𝑝7)𝑆(𝑝8)=0.0260
	CA11=CA12=𝑆(𝑝10)=0.45	CA11=CA12=𝑆(𝑝10)=1
Connection availability of the networks	(0.625+0.625+0.281+0.281+0.567+0.255+0.026+0.45+0.45)/9=0.3956	(0.6539+0.6539+0.2017+0.2017+0.3165+0.0732+0.0260+1+1)/9=0.4585
Relaying costs	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)=7.001𝑃max	2𝑢(0.6539𝑃max)+2𝑢(0.6539𝑃max+0.3085𝑃max)+𝑢(0.3165𝑃max)+𝑢(0.3165𝑃max+0.2313𝑃max)+𝑃max𝑢(0.3165𝑃max+0.2313𝑃max+0.3550𝑃max)+2𝑢(𝑃max)=6.9997𝑢