Skip to main content

Table 6 The values of \((q^*_S, q^*_C, q^*_D)\) that maximize the weighted sum throughput \(T_w\) for different values of \(M_U\) when \(\alpha = 0.7\) and the queue at S is stable

From: A wireless caching helper system with heterogeneous traffic and random availability

\(\delta = 0.5\)

\(M_U\)

 

\(w = 1/4\)

\(w = 2/4\)

\(w = 3/4\)

200

max. \(T_w\)

0.227

0.285

0.342

\((q^*_S, q^*_C, q^*_D)\)

(0.999, 1, 1)

(0.999, 1, 1)

(0.999, 1, 1)

400

max. \(T_w\)

0.224

0.283

0.341

\((q^*_S, q^*_C, q^*_D)\)

(0.801, 1, 1)

(0.824, 1, 1)

(0.769, 1, 1)

600

max. \(T_w\)

0.221

0.281

0.340

\((q^*_S, q^*_C, q^*_D)\)

(0.756, 1, 1)

(1, 1, 1)

(1, 1, 1)

800

max. \(T_w\)

0.219

0.279

0.340

\((q^*_S, q^*_C, q^*_D)\)

(1, 1, 1)

(1, 1, 1)

(0.746, 1, 1)

1000

max. \(T_w\)

0.217

0.278

0.339

\((q^*_S, q^*_C, q^*_D)\)

(0.732, 1, 1)

(1, 1, 1)

(1, 1, 1)

\(\delta = 1.2\)

    

200

max. \(T_w\)

0.145

0.230

0.315

 

\((q^*_S, q^*_C, q^*_D)\)

(0.713, 1, 1)

(0.713, 1, 1)

(0.713, 1, 1)

400

max. \(T_w\)

0.135

0.223

0.312

 

\((q^*_S, q^*_C, q^*_D)\)

(1, 1, 0)

(0.999, 1, 0)

(0.999, 1, 0)

600

max. \(T_w\)

0.129

0.220

0.310

 

\((q^*_S, q^*_C, q^*_D)\)

(1, 1, 0)

(1, 1, 0)

(1, 1, 0)

800

max. \(T_w\)

0.126

0.217

0.309

 

\((q^*_S, q^*_C, q^*_D)\)

(1, 1, 0)

(1, 1, 0)

(1, 1, 0)

1000

max. \(T_w\)

0.123

0.216

0.308

 

\((q^*_S, q^*_C, q^*_D)\)

(1, 1, 0)

(1, 1, 0)

(0.540, 1, 0)