Table 1 List of notations for mathematical analysis of BRIDGE protocol
From: A gating mechanism for border node assisted association of wireless personal area networks
Notation | Description | Notation | Description |
|---|---|---|---|
T total | Delay from Ns in PAN A to Nr in PAN B | T qo | Queuing delay at ordinary node |
T 1 | Delay from Ns to PAN coordinator A | T q (av) | Av. queuing delay at bridge node |
T PA | Total processing delay at PAN coordinator A | T qb | Queuing delay at bridge node |
T 2 | Delay from PAN coordinator A to connect node | Λ | Data arrival rate at a node |
T b | Total delay at bridge node | M | Data processing rate at a node |
T switch | Delay at bridge node due to switching WPANs | N b | Number of packets requested by PAN B |
T 3 | Total delay from bridge node to Nr in WPAN B | T A | Time at bridge node in home PAN A |
h 1 | Hop count from Ns to PAN coordinator A | T B | Time at bridge node in PAN B |
h 2 | Hop count from PAN coordinator A to bridge node | D r | Inter-WPAN data at bridge node |
P a | Probability that Ns has data to send | D i | Intra-WPAN data at bridge node |
T s | Transmission time for successful transmission | λ 1 | Arrival rate of sensed data at a node |
T c | Time for unsuccessful transmission of packet | λ 2 | Arrival rate of data to be relayed |
E[a] | Av. # of attempts for successful packet transmit | N i | Number of neighbors of node i |
P s | Probability of successful transmission b/w nodes | P ij | Probability data from node j is for i |
P tr | Probability of transmission attempt | λ B | Data arrival rate at a bridge node |
m | Max unsuccessful attempts →packet is dropped | λ t | Data rate from PAN A to PAN B |
M | No. of neighbors of nodes transferring data | b | Number of border (bridge) nodes |