Table 2 Symbol interpretation

\(\alpha _1\) and \(\alpha _2\)

two critical angles

\(R_e\)

Earth radius

\(\left( \tau _1, \gamma _1\right)\)

the longitude and latitude

\(\left( \tau _2, \gamma _2\right)\)

the geodetic coordinates

\(d_c\)

the inter-satellite distance

\(P_r\)

the received signal power

\(d_i\)

the input data size of task\(_i\)

\(\lambda _m\)

IMD task arrival rate

\(\theta\)

the offloading rate(a prior parameter)

\(\lambda _{\text{ Sat }}\)

Sat-MEC server initial task arrival rate

\(\gamma\)

the discount factor

\(L_s\)

the signal path loss

\(\Phi\)

tasks scheduling policy

\(\chi ^j\)

the environment’s state

\(\Phi ^*\)

tasks scheduling policy

\(\chi ^{\prime }\)

the next environment state

\(B_0\)

the bandwidth on C-band

\(\sigma ^2\)

Gaussian white noise power

\(f^m\)

computational capacity of IMD

\(w(\chi , a)\)

the utility function

\(V(\chi )\)

the optimal value of the state \(\chi\)

\(B_{T S T}\)

the bandwidth on the Ka-band

\(c_i\)

the number of CPU cycles for task\(_i\) computation

\(f^s\)

the number of cpu cycles per second

EIRP

equivalent isotropically radiated power

\(G_r\)

the gain of satellite receiving antenna

\(b_i^{\text{ up } }\) and \(b_i^{\text{ down } }\)

the data size of \(\textrm{task}_i\) uplink and downlink

\(V(\chi , \Phi )\)

the state value function of the Agent

\(S_{T S T}\)

the signal power from TST to satellite

\(G_t\)

the gain of the satellite transmitting antenna

\(Q_s\)

the initial task queue backlog at current time

\(T_i^{u p}\) and \(T_i^{\text{ down } }\)

transmission time for task\(_i\) uplink and downlink

\(\Phi _{(a)}\)

the corresponding tasks scheduling methods

\(a_n(\textrm{t})\)

the action of \(\textrm{task}_i\) being scheduled to satellite s.

\(f^s\)

the number of cpu cycles per second for processing tasks on LEO satellite s

\(N_{T S T}\)

the interference experienced by the over-the-top satellite on the sub-carrier