Table 1 Notations
From: Priority queueing models for cognitive radio networks with traffic differentiation
Notation | Description |
|---|---|
Y | Length of operating periods (RV) |
R | Length of recovery (interruption) periods (RV) |
C | C = Y + R |
λ | Packet arrival rate |
A | packet inter-arrival time (RV) |
X | Completion time (RV) |
X ∗ | Completion time in alternative model (RV) (Section 3.4) |
Index b | For packets entered a busy system |
Index e | For packets entered an empty system |
Index a | For packets entered an empty-available system |
Index u | For packets whose service started at the beginning of a Y |
B | HP busy periods (RV) |
B b | Busy period started with X b |
B Z | Busy period started with Z + X b |
T | Real service time (RV) |
J | Remaining completion time of the packet in service |
| LST of a continuous random variable Z |
f Z (t) | PDF of a random variable Z |
F Z (t) | CDF of a random variable Z |
m(t) | Average number of renewals until time t |
ma|b|u(t) | m(t) for packets of type a, b, or u |
m2(t) | Second moment of the number of renewals until time t |
ρ | λ E[X] |
ρ b | λ E[X b ] |
P ae | Probability of system being available when empty (arrival point) |
W | Waiting time in the queue |
W ∗ | Waiting time for the alternative model |
D | Total time spent in the system |
P aiC|Y|R | Probability of HP arrival in a cycle (C), Y, or R |
K | Local parameter to count the number of an event |
i = 1,2 | Subindex represents the traffic class |
α | Exponentially distributed parameter when F Y = 1 - e-αt |
β | Exponentially distributed parameter when F R = 1 - e-βt |
| Min. of random variable Z and an exponentially distributed (Eq. 4) |
γ | Exponentially distributed parameter when F T = 1-e-γt |
N p | Number of priority classes |
T v | Service time of virtual packets which form the interruptions |
P A<C | Probability of arrival in C = P r(A < C) |
R r | Remaining of R after an arrival in R |
C r | Remaining of C after an arrival in C |
| Z1|(Z1 < Z2) (for two RVs) |
S | Initial setup time (RV) (Section 3.5) |
P 0 | Probability of system being empty |
P L|N H | Probability of system being empty of HP but not LP |