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Table 1 Notation in problem formulation

From: SINR-based scheduling in multi-path multi-hop multi-radio multi-channel mmWave WPANs

Symbol

Description

K

The number of pairings in a schedule

V

The number of flows in the network

M v

The number of paths of the v-th flow

H vp

The number of hops of the p-th path of the v-th flow

d v

The traffic demand of the v-th flow

d vp

The traffic demand distributed to the p-th path

l vpi

The i-th link of the p-th path of the v-th flow

c vpi

The transmission rate of link l vpi

L uqj

The set of tuple links of link l vpi

\({l_{vpi}^{x}}\)

The x-th tuple link of link l vpi

t vpi

The transmitter of link l vpi (tuple link \({l_{vpi}^{x}}\))

r vpi

The receiver of link l vpi (tuple link \({l_{vpi}^{x}}\))

\(a_{vpi}^{k}\)

A binary variable to indicate whether link l vpi is scheduled in the k-th pairing

\(a_{vpi}^{xk}\)

A binary variable to indicate whether tuple link \({l_{vpi}^{x}}\) is scheduled in the k-th pairing

\(\textbf {R}_{{t_{pi}}}\)

The set of radios of node t vpi

C

The set of channels in the network

\({W_{vpi,uqj}^{x,y}}\)

The interference level of tuple link \({l_{vpi}^{x}}\) caused by \({l_{uqj}^{y}}\)