--- title: "GOS vs blocking; 600 calls, 2.5 min" subject: "Telecommunications" chapter: 6 key: "semester_8/telecommunications:gos-blocking-600-calls-2-5min" source: https://www.bctengineer.com/q/semester_8/telecommunications/gos-blocking-600-calls-2-5min site: BCT Engineering --- # GOS vs blocking; 600 calls, 2.5 min Telecommunications · Chapter 6: Telephone Traffic - Asked in: 2078 Bhadra, 2+6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/gos-blocking-600-calls-2-5min - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6 ## Question How do you define and differentiate between Grade of Service (GOS) and Blocking Probability (PB)? During a busy hour 600 calls were offered to a group of trunks and 40 calls were lost. If the average call duration was 2.5 minutes, find the offered traffic, carried traffic, lost traffic, Grade of Service and total duration of congestion. ## Short answer GoS = lost/offered calls; blocking probability is model-based probability all servers busy. 600 offered, 40 lost, h=2.5 min (1/24 h): offered = 600/24 = 25 E; carried = 560/24 = 23.33 E; lost = 40/24 = 1.67 E; GoS = 40/600 = 0.0667; congestion time = 0.0667×3600 = 240 s. ## Answer #### GoS vs blocking probability - **Grade of Service (GoS):** the fraction of offered calls that are lost in the busy hour, $GoS = \dfrac{\text{calls lost}}{\text{calls offered}}$. It is a service-quality target or measurement for a route or the whole connection. - **Blocking probability ($P_B$):** the probability, from a traffic model, that all servers are busy (time congestion) or that an arriving call is blocked (call congestion), e.g. from Erlang B. | GoS | Blocking probability | |---|---| | Measured/specified quality | Calculated probability | | Ratio of lost to offered calls | Probability all servers busy | | May cover many links end to end | Usually one server group | | Design target (e.g. 0.01) | Used to find N to meet target | For Poisson traffic in a loss system the two are numerically equal. **Given:** calls offered $C_o = 600$, calls lost $C_l = 40$, mean holding time $h = 2.5\ \text{min} = \tfrac{1}{24}$ h, period T = 1 h. Traffic in Erlangs $= \dfrac{\text{calls} \times h}{T}$. #### (a) Traffic offered $$ \begin{aligned} A_o &= \frac{C_o\,h}{T} = 600 \times \tfrac{1}{24} \\ &= 25\ \text{E} \end{aligned} $$ #### (b) Traffic carried Calls carried $= 600 - 40 = 560$ $$ \begin{aligned} A_c &= 560 \times \tfrac{1}{24} = 23.33\ \text{E} \end{aligned} $$ #### (c) Traffic lost $$ \begin{aligned} A_l &= A_o - A_c = 40 \times \tfrac{1}{24} = 1.67\ \text{E} \end{aligned} $$ #### (d) Grade of service $$ \begin{aligned} GoS &= \frac{C_l}{C_o} = \frac{40}{600} = 0.0667 \end{aligned} $$ #### (e) Duration of congestion For pure-chance (Poisson) traffic the proportion of time all trunks are busy (time congestion) equals the proportion of calls lost (call congestion), so congestion time in the busy hour is $$ \begin{aligned} T_c &= GoS \times 3600\ \text{s} = \frac{40}{600} \times 3600 \\ &= 240\ \text{s} \end{aligned} $$ **Answer:** offered traffic = **25 E**, carried = **23.33 E**, lost = **1.67 E**, GoS = **0.0667**, congestion duration = **240 s (4 min)**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which statement correctly separates GoS from blocking probability? A. GoS is the measured or specified ratio of lost to offered calls; PB is calculated from a traffic model B. GoS is calculated from Erlang B; PB is counted from lost calls C. They are always different numerically D. GoS applies only to delay systems Answer: A. GoS is a quality target or measurement; PB comes from a model, and for Poisson traffic they are numerically equal. (Key point: GoS vs PB) 2. 600 calls of 2.5 min in one hour give what offered traffic? A. 240 E B. 25 E C. 15 E D. 1500 E Answer: B. 600 x 2.5 / 60 = 25 E. (Key point: Offered traffic) 3. With 40 of 600 calls lost, what are GoS and congestion time? A. 0.0667 and 40 s B. 0.04 and 144 s C. 0.0667 and 240 s D. 0.0667 and 3600 s Answer: C. GoS = 40/600 = 0.0667; time = 0.0667 x 3600 = 240 s. (Key point: GoS and congestion) ## Close variants set in other exams - [Traffic numerical: 1000 calls, 5 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-1000-calls-5-lost) — Telecommunications, chapter 6, asked 6× - [Traffic numerical: 1200 calls, 6 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-1200-calls-6-lost) — Telecommunications, chapter 6, asked 6× - [Traffic numerical: 800 calls, 50 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-800-calls-50-lost) — Telecommunications, chapter 6, asked 6× - [Traffic numerical: 600 calls, 40 lost, 120 s](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-600-calls-120s) — Telecommunications, chapter 6, asked 5× - [GOS numerical: 1400 calls, 14 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-busy-hour-1400-calls) — Telecommunications, chapter 6, asked 5× ## Related in Telecommunications - [Trunk group numerical: 40 E, 20 s, 4 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atrunks-40e-20s-four-lost) — Telecommunications, chapter 6, asked 2× - [Trunk group numerical: 30 E, 12 s, 2 lost](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atrunks-30e-12s-two-lost) — Telecommunications, chapter 6, asked 2× - [GOS vs blocking probability; E.164 plan](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-vs-blocking-e164) — Telecommunications, chapter 6 - [Traffic intensity, GOS and call duration probability](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atraffic-intensity-call-duration-probability) — Telecommunications, chapter 6 - [GOS and blocking probability in a loss system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-blocking-loss-system) — Telecommunications, chapter 6 - [E.600 busy hour, NTA duties and ITU sectors](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ae600-busy-hour-nta-itu) — Telecommunications, chapter 7