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Table 1 Symbols used for single traffic source

From: Random access with adaptive packet aggregation in LTE/LTE-A

Notation Definition
S j, i State in Semi-Markov process
N Packet aggregation threshold
λ Packet arrival rate
p j Unsuccessful probability for the jth preamble transmission
M Transmission limit for random access
W Backoff window size
\(p_{j}^{\prime }\) Error probability caused by wireless channel for the jth preamble transmission
p c Preamble collision probability
π j, i Stationary probability for state S j, i
p E, j Probability that a preamble collision cannot be detected by eNB for the jth random access
E i, j Probability that a preamble cannot be decoded by eNB when it is sent by i+1 UEs for the jth random access
τ Probability that as UE is sending a preamble in one subframe
N C Amount of preamble allocated for contention based random access
N M Amount of devices in the cell
T E Duration that starts when the UE sends a preamble and ends at the end of the random access response window
T C Duration that starts when the UE sends a preamble and ends when the contention resolution timer expires
T S Duration that starts when the UE sends a preamble and ends when a UE receives the contention resolution message from eNB
h j Average state holding time for state S j, 0
Q j Proportion of time that a UE is at state S j, 0
T Average state holding time for all states
\(T_{j}^{\prime }\) Duration for an unsuccessful random access at the jth try
T j Channel access latency if the aggregated packet is successfully delivered at jth try
d Expected time used to deliver an aggregated packet
d Overall latency for the first aggregated packet
α Packet loss rate limit
N max Maximum allowed amount of aggregated packets
β Power saving factor to measure energy saving with packet aggregation
d 0 Time used for one random access with packet aggregation