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Консультация № 195370
24.04.2019, 14:48
0.00 руб.
11.02.2020, 15:58
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
На систему M/M/1 в каждую секунду поступает 40 вызовов.
Среднее время обслуживания равно 10 миллисекунд.
Чему равно среднее число вызовов находящихся в системе?
На систему M/M/1 в каждую секунду поступает 40 вызовов.
Среднее время обслуживания равно 10 миллисекунд.
Чему равно среднее число вызовов находящихся в системе?
Обсуждение
27.04.2019, 16:13
общий
это ответ
Здравствуйте, anny!
Поскольку задано "каждую секунду поступает 40 вызовов", то Период следования вызовов равен
T=1сек / 40 = 25 мСек.
Из них "Среднее время обслуживания равно 10 миллисекунд". Значит, искомое "среднее число вызовов находящихся в системе" равно скважности импульсов - отношению длительности импульса к его периоду :
Nс = [$964$] / T = 10 мС / 25 мС = 0,4
Как проверить правильность этой формулы ? Представим, будто система может обслуживать т-ко 1 вызов, но получает их в избытке. Тогда накапливается такая очередь вызовов, что среднее число вызовов находящихся в системе стабильно Nс=1 .
При прежнем значении Среднего времени обслуживания [$964$]=10 мС пропускная способность системы будет Nп=1 сек / 10мСек = 100 вызовов / сек. А их период следования T = 1000мС / Nп = 10 мС.
Выше-предложенная Формула вычисления среднего числа вызовов находящихся в системе
Nс = [$964$] / T = 10 мС / 10 мС = 1 подтвердилась для тестового режима.
А может, Ваша система действительно может обслуживать т-ко 1 вызов, и при случайно-одновременном поступлении 3х вызовов они будут обработаны поочерёдно с микро-задержкой, незаметной для абонента (как и было много лет на телефонных станциях).
Поскольку задано "каждую секунду поступает 40 вызовов", то Период следования вызовов равен
T=1сек / 40 = 25 мСек.
Из них "Среднее время обслуживания равно 10 миллисекунд". Значит, искомое "среднее число вызовов находящихся в системе" равно скважности импульсов - отношению длительности импульса к его периоду :
Nс = [$964$] / T = 10 мС / 25 мС = 0,4
Как проверить правильность этой формулы ? Представим, будто система может обслуживать т-ко 1 вызов, но получает их в избытке. Тогда накапливается такая очередь вызовов, что среднее число вызовов находящихся в системе стабильно Nс=1 .
При прежнем значении Среднего времени обслуживания [$964$]=10 мС пропускная способность системы будет Nп=1 сек / 10мСек = 100 вызовов / сек. А их период следования T = 1000мС / Nп = 10 мС.
Выше-предложенная Формула вычисления среднего числа вызовов находящихся в системе
Nс = [$964$] / T = 10 мС / 10 мС = 1 подтвердилась для тестового режима.
А может, Ваша система действительно может обслуживать т-ко 1 вызов, и при случайно-одновременном поступлении 3х вызовов они будут обработаны поочерёдно с микро-задержкой, незаметной для абонента (как и было много лет на телефонных станциях).
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