--- title: "Succession of events; GPSS telephone model" subject: "Simulation and Modeling" chapter: 9 key: "semester_8/simulation_and_modeling:gpss-telephone-system" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/gpss-telephone-system site: BCT Engineering --- # Succession of events; GPSS telephone model Simulation and Modeling · Chapter 9: Simulation software - Asked in: 2069 Bhadra (old course), 2+8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/gpss-telephone-system - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-9 ## Question Define the succession of events. Design a telephone system simulation model using GPSS symbols and explain in brief. ## Short answer Succession of events: call arrival, line seizure, conversation, release. GPSS model: STORAGE 5; GENERATE 10,5; GATE SNF checks if storage not full, lost calls counted; ENTER, ADVANCE 40,10, LEAVE. Blocking probability = lost/total calls. ## Answer #### Succession of events A succession of events is the chain of events in time order in which one event leads to the next. In a simulation, an event happens at a time, changes the system state, and may schedule future events. For a telephone call the chain is: call arrives -> line seized (or call lost) -> conversation -> call ends -> line freed -> next waiting call starts. The simulation clock jumps from one event to the next in this sequence. #### Telephone system model Assumptions: a small exchange has 5 trunk lines. Calls arrive every 10 s on average (uniformly between 5 and 15 s, as given by `GENERATE 10,5`); a call lasts 40 s on average (uniform 30 to 50 s). If all lines are busy, the call is **lost** (blocked). We want the fraction of lost calls and the line utilisation. GPSS blocks: ```text LINES STORAGE 5 GENERATE 10,5 ; calls arrive GATE SNF LINES,LOST ; if lines full, go to LOST ENTER LINES ; occupy a line ADVANCE 40,10 ; conversation LEAVE LINES ; free the line SAVEVALUE DONE+,1 TERMINATE 1 LOST SAVEVALUE BLOCKED+,1 ; lost call counter TERMINATE 1 START 1000 ``` If a single exchange facility is used, `SEIZE`/`RELEASE` take the place of `ENTER`/`LEAVE`. `TRANSFER BOTH` can also be used to try a second route. #### Block diagram ```text GENERATE -> GATE SNF -+-> ENTER -> ADVANCE -> LEAVE (calls) (line free?) | (take (talk) (free) | line) | | TERMINATE +--no--> SAVEVALUE (lost) | TERMINATE ``` #### Explanation Each call is a transaction that follows the succession of events above: arrival, seizing a line, talking, release. A call that finds all lines busy takes the other route and is counted as lost. - `GENERATE 10,5` creates call transactions, one every 10 ± 5 s. - `GATE SNF` tests whether the storage is not full. If it is full, the call goes to the LOST branch. - `ENTER` and `LEAVE` take and free one line; the storage can have up to 5 users. - `ADVANCE` represents the conversation time. - `TERMINATE 1` ends the call; `START 1000` stops the run after 1000 transactions. - Output: storage utilisation, maximum content, average content, and the count of lost calls. Blocking probability = BLOCKED / total calls. #### Quick check of the numbers Offered traffic = mean talk time / mean inter-arrival time = 40/10 = 4 Erlangs on 5 lines. For Poisson (exponential) arrivals, Erlang-B gives a blocking probability of about 0.2 (20%) for A = 4, N = 5, and a line utilisation of about 4 x (1 - 0.2)/5 = 0.64. The uniform arrivals of `GENERATE 10,5` are more regular than Poisson arrivals, so the simulated blocking will be somewhat lower than 20%. To compare directly with Erlang-B (verification), replace the GENERATE block with exponential inter-arrival times of mean 10 s (for example `GENERATE RVEXPO(1,10)` in GPSS/H). If the simulated figures are then far from these values, the model should be re-examined. More lines can be added to see how the blocking falls, which is the design question for the exchange. #### Assumptions Calls are independent, lost calls do not retry, there is no ringing time, and all lines are identical. The talk time is taken as uniform 30 to 50 s for simplicity; an exponential time could be used instead. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is a succession of events? A. A random set of independent events B. A list of statistics C. The set of random numbers used D. A time-ordered chain in which one event leads to the next, changing state and scheduling future events Answer: D. Events occur in time order, each changing state and possibly scheduling later events. (Key point: Succession of events) 2. How does the model handle a call when all 5 lines are busy? A. GATE SNF sends it to LOST where it is counted and terminated B. It waits in a queue C. It is placed on a sixth line D. It is delayed by ADVANCE Answer: A. GATE SNF tests that the storage is not full; if full the call branches to LOST and is counted as blocked. (Key point: Lost call logic) 3. Why are ENTER and LEAVE used instead of SEIZE and RELEASE? A. They create transactions B. They are faster C. The storage has 5 lines (multi-server), whereas a facility holds only one user D. They record queue statistics Answer: C. ENTER/LEAVE use a storage of capacity 5, while SEIZE/RELEASE handle a single server. (Key point: ENTER/LEAVE) 4. With mean inter-arrival 10 s and mean talk 40 s, what is the offered traffic? A. 0.25 Erlangs B. 4 Erlangs C. 50 Erlangs D. 5 Erlangs Answer: B. Offered traffic = 40/10 = 4 Erlangs, giving Erlang-B blocking of about 0.2 on 5 lines. (Key point: Offered traffic) ## Related in Simulation and Modeling - [Five GPSS block diagram symbols](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Agpss-block-symbols) — Simulation and Modeling, chapter 9, asked 2× - [Define system, model, simulation](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Asystem-model-simulation-define) — Simulation and Modeling, chapter 1 - [GPSS manufacturing shop, conditional transfer](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Agpss-manufacturing-shop) — Simulation and Modeling, chapter 9 - [Simulation of computer system serving WWW](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Acomputer-system-www-request) — Simulation and Modeling, chapter 10, asked 2× - [Continuous system simulation; analog computer example](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Acontinuous-simulation-analog-example) — Simulation and Modeling, chapter 3 - [CPU simulation with example](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Acpu-simulation-example) — Simulation and Modeling, chapter 10, asked 4× ## Related in other subjects - [FDM hierarchy in telephone system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afdm-hierarchy-telephone) — Data Communication, chapter 6 - [Digital communication system; Shannon-Fano for six symbols](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adcs-block-shannon-fano-six) — Communication Systems, chapter 6 - [Pure loss system and binomial model](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apure-loss-binomial-model) — Telecommunications, chapter 6 - [Pure loss system and Engset model](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apure-loss-engset-model) — Telecommunications, chapter 6