A simple telephone system consists of two end offices and a...

A simple telephone system consists of two end offices and a single toll office to which each end office is connected by a 1-MHz full-duplex trunk. The average telephone is used to make four calls per 8-hour workday. The mean call duration is $6 \mathrm{~min}$. Ten percent of the calls are long distance (i.e., pass through the toll office). What is the maximum number of telephones an end office can support? (Assume $4 \mathrm{kHz}$ per circuit.) Explain why a telephone company may decide to support a lesser number of telephones than this maximum number at the end office.

Key Concepts

Telephone Traffic Engineering

Telephone traffic engineering involves analyzing the patterns of call arrivals, durations, and usage to determine the required capacity in a network. This field uses techniques such as Erlang calculations to estimate the required number of circuits or channels in order to support a given number of users while keeping the probability of call blocking within acceptable limits.

Trunk Capacity and Channel Bandwidth

In a telephone system, a trunk is a communication link that carries multiple calls simultaneously between exchanges. The capacity of a trunk is determined by dividing its overall bandwidth into smaller channels (each requiring a specific bandwidth). Understanding how to allocate bandwidth per circuit is crucial to ensuring that the network can support the predicted call volume.

Full-Duplex Communication

Full-duplex communication allows simultaneous two-way transmission of voice signals. This concept is especially important in telephony, as it means that both parties in a call can speak and listen at the same time without interference, affecting how trunks are designed and utilized.

Peak Load and Blocking Probability

Peak load refers to the time when the telephone system experiences the highest volume of concurrent calls. Engineering the system to handle peak load involves calculating the necessary number of circuits to keep the blocking probability (the chance that a caller finds all circuits busy) low. This often leads designers to offer less than the theoretical maximum number of subscribers to maintain service quality during busy periods.

Usage Patterns and Subscriber-to-Circuit Ratio

Usage patterns such as call frequency per subscriber and average call duration are key factors in determining a practical subscriber-to-circuit ratio. While calculations might suggest a maximum number of telephones based on available circuits, operators often choose to support fewer subscribers to accommodate fluctuations in calling behavior and to ensure reliable service.

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