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Table 6 List of parameters and symbols used in the paper

From: Network dimensioning and base station on/off switching strategies for sustainable deployments in remote areas

Λ v(h),Λ d(h)

Rate of voice and data connection requests at hour h per user

λ v(h),λ d(h)

Aggregated rate of voice and data connection requests at hour h

1/μ v,1/μ d

Mean duration of a voice and data connection

R v,R d

Bit rate of an individual voice and data connection

F v,F d

Spreading factor for a voice and data connection

N U

Number of users

E b /N 0

Energy per bit to noise power spectral density

\(\gamma _{ji}^{\text {UL}},\gamma _{ij}^{\text {DL}}\)

Minimum threshold quality (target) for E b /N 0 in UL and DL for the j-th user at the i-th carrier

W

Chip rate

S i

Number of users connected simultaneously to the i-th carrier

\(P_{ji},\bar {P}_{ji}\)

Power (and its mean value) transmitted by the j-th user at the i-the carrier in UL

G ji

Equivalent gain between the j-th user and the SC (i-th carrier)

X ji

Channel fading between the j-th user and the SC (i-th carrier)

R j

Bit rate associated to the service of the j-th user

\(\eta _{i}^{\text {UL}},\eta _{i}^{\text {DL}}\)

UL and DL load factors at the i-th carrier

ν j

Activity factor associated to the service of thej-th user

α j

Orthogonality factor in the DL associated to the j-th user

\({\sigma _{i}^{2}},{\sigma _{j}^{2}}\)

Noise power at the SC receiver (i-th carrier) and at the receiver of the j-th user

\(P_{i}^{\text {Ca}},\bar {P}_{i}^{\text {Ca}}\)

Total power (and its mean value) transmitted in the DL at the i-th carrier

\(P_{i}^{\text {cCH}}\)

Power assigned to the DL common channels at the i-th carrier

E c /I 0

Energy per chip to received interference power spectral density

γ cpich

Minimum threshold quality (target) for E c /I 0 for the common channels

\(P_{\max }^{\text {UE}}\)

Maximum available power at the UE

PCH(n,m)

Power control headroom for n voice and m data connections

\(P_{\max }^{\text {Ca}}\)

Maximum available power at the SC for each carrier

\(P_{n,m}^{\text {cov}}\)

Coverage probability for n voice and m data connections

\(P_{n\rightarrow n+1,m}^{\text {cov}}\)

Conditional coverage probabilities

\(P_{n,m\rightarrow m+1}^{\text {cov}}\)

 

(n,m)

Index of states in the 2D M/M/m/m Markov chain

(n,m,k,l)

Index of states in the 4D M/M/m/m Markov chain

P n,m ,P n,m,k,l

State probabilities of the 2D and 4D Markov chains

\(\lambda _{n\rightarrow n+1,m}^{\text {v}}\)

Birth rates in the Markov chain for configuration #1

\(\lambda _{n\rightarrow n+1,m}^{\text {d}}\)

 

\(\lambda _{n\rightarrow n+1,m,k,l}^{\text {v}}\)

Birth rates in the Markov chain for configuration #2

\(\lambda _{n,m,k\rightarrow k+1,l}^{\text {v}}\)

 

\(\lambda _{n,m\rightarrow m+1,k,l}^{\text {d}}\)

 

\(\lambda _{n,m,k,l\rightarrow l+1}^{\text {d}}\)

 

\(\hat {C}_{\text {v}},\hat {C}_{\text {d}}\)

Maximum number of voice and data connections in configuration #1

\(\hat {C}_{\text {v}}^{A},\hat {C}_{\text {d}}^{A}\)

Maximum number of voice and data connections for both carriers in configuration #2

\(\hat {C}_{\text {v}}^{B},\hat {C}_{\text {d}}^{B}\)

 

C T

Maximum number of simultaneous connections supported by a carrier

N,M

Final decision for the dimensioning of the maximum number of voice and data connections

\(\mathcal {S}\)

Set of all possible states in the Markov chain

\(\mathcal {A}_{i}\)

Disjoint subsets in the Markov chains

\(\hat {P}_{C}^{\text {v}},\hat {P}_{C}^{\text {d}}\)

Voice and data congestion probabilities

\(\hat {P}_{B}^{\text {v}},\hat {P}_{B}^{\text {d}}\)

Voice and data blocking probabilities

\(\Gamma _{B}^{\text {v}},\Gamma _{B}^{\text {d}}\)

Maximum target voice and data blocking probabilities

\(\hat {T}_{T}=f\)

Function relating the maximum number of voice and data connections and the required backhaul bandwidth

P R (h)

Instantaneous radiated power at hour h

f(P R |h)

PDF of the instantaneous radiated power at hour h

P rad(h)

Average radiated power at hour h

P c

Consumed power

P sleep,P 0

Parameters of the power consumption model

Δ p

 

L

Total average energy consumption in one day

E SP

Total energy that the solar panels should generate in one day

η G

Energy loss due to the inefficiency of the solar panels

f c

Energy correction factor for the working of the solar panels

P nom

Nominal power of a solar panel

G dm

Average daily solar radiation during the worst month of the year

C B

Total capacity required for the batteries

\(P_{\max }^{d}\)

Percentage of battery that can be spent for a proper operation

C 1

Capacity of a single battery

n B

Number of required batteries

λ TH

Threshold on the traffic rate for a single type of traffic

λ TH

Threshold frontier on the traffic rate for two types of traffic

P 1Ca,P 2Ca

Mean power required with 1 carrier and 2 carriers active

λ[m]

Traffic rate at the m-th time instant within the day

p[m]

Error in the knowledge of the traffic rate at the m-th time instant

\({\sigma _{p}^{2}}\)

Variance of the error in the knowledge of the traffic rate

T

Time lapse between consecutive time instants

M

Number of time instants used for measuring the traffic

λ ML

ML estimation of the traffic rate

t w

Worst-case time instant for the calculation of the threshold

\(\bar {P}_{\text {out}}\)

Bayesian robust outage probability

θ

Maximum admissible outage probability