A repair man fixes broken televisions.There pair time is exponentially distributed with A mean of 30 minutes. Broken televisions arrive at his repair shop according to a Poisson stream, on average 10 broken televisions perday (8hours).
(i) What is the fraction of time that the repair man has no work to do?
(ii) How many televisions are, on average, at his repair shop?
(iii) What is the mean through put time (waiting time plus repair time) of a television ?
- Rata-rata service time E(B) = 1/µ = 1/2 (dengan satuan waktu : jam),
arrival rate (l) = 10/8 (10 televisi rusak per 8 jam per hari),
Server Utility / jumlah yang dilayani (r) = l/µ = (10/8)/2 = 5/8,
Maka waktu tersisa tanpa ada pekerjaan adalah 1-r = 1 – 5/8 = 3/8
2. Rata-rata jumlah televisi di toko reparasi E(L) = r / (1-r) = (5/8)/(3/8) = 5/3
3. Troughput time/ sojourn time = E(S) = (1/µ) / (1-r) = ½ / (3/8) = 4/3 jam = 80 menit