Table 1 The notations with its descriptions used in the proposed SMPISCS

N _s

Number Of Sensor Nodes In The Network

T_S ∗ T_S

Terrain Area

d _s

Inter-communication distance between sensor nodes

d _re

Reachable inter-communication distance between sensor nodes

E _e

Energy consumed for sending data in the free path

E _trans

Energy consumed for transmission

E _amp

Energy consumed for sending data in the multi-fading path

E _fuse

Energy consumed for sending data under fused path

l

Length in Bits of data

(C, S)

Sensor node with cooperative state and has possibility of transiting into its selfish state

C _r

The threshold energy probability of sensor nodes

1 − C_s

The complementary threshold energy probability of sensor nodes

β

Failure time of the sensor node operating in normal mode

β _s

Time to failure of the selfish nodes

μ

Time to re-energize the failed node to turn into a reliable mode

π _{C, S}

Transition probability of a sensor node from cooperative state to its selfish state

π _NC

Transition probability of a sensor node from non cooperative state to its cooperative state

π _{F, F}

Transition probability of a sensor node from failure state that could not be rehabilitated

π _{C, C}

Transition probability of a sensor node to retain its cooperative state

U_d(0, T)

Uniformly distributed probe diagnostic time

ST _i

Sojourn time

PT _{( i,  j)}

General probability representing the transition of sensor node from one state to another

(F, F)

Sensor node with failure state and has no possibility of transiting into its cooperative state

(C, F)

Sensor node from cooperative state to its failure state

S _i

Sojourn time state

T _PR

Threshold probe diagnostic time

(N, C)

Sensor node from cooperative state to its non cooperative state

(N, D)

Sensor node from defective state to its cooperative state