Discussions with people familiar with the telecommunications/ISP industries indicate that assumptions for Debt Percent and Cost of Debt are reasonable for the business being represented in this model.31 Sensitivity analysis of the Cost of Capital is presented in Chapter 4.
The economic life of capital equipment can vary greatly depending on the type of equipment and the business in which it is being used. For example, fiber optic cable installed throughout a city might last 20-30 years. However, the laser equipment terminating the fiber might only last five years because of advances in laser technology such that more bandwidth can be obtained from the same fiber.
Similarly for an ISP, its computers and telecommunications equipment change rather rapidly. For the model, it is assumed that the economic life of each piece of capital equipment if 36 months. This is also the value used by BBN for similar assets.32
Calculations converting a one-time cost into a monthly cost are carried out for each piece of capital, and the results are presented in the section describing the piece of capital.33
varies depending on how concerned each ISP is with its dial-in subscribers experiencing busy signals when calling.34
Implied in this rule of thumb is a user profile of the average holding time and the average call arrival rate during peak the period (because the number of modems is sized based on the peak demand). If either of these numbers changed (while holding the number of subscribers constant), the required number of modems would need to change to avoid blocking, and hence, the ratio of subscribers per modem would change. Consequently, simply using a subscriber per modem ratio to determine the number of modems is not necessarily accurate if certain assumptions about dial-in behavior change. Instead of the ratio, the Erlang B (also called the Erlang Loss) formula can be used to determine the appropriate number of modems needed to satisfy a blocking probability.
Let c be the number of modems, ρ be the offered load, subs be the number of subscribers, percent be the percent of subscribers that call during the peak hour and hold be the average holding time per call. Call arrivals are assumed to be Poisson, and holding times are assumed to follow a general distribution (i.e., call lengths are stationary, independent and identically distributed).35 The load is found by the following formula:
34 For comparison, as of January 1997, AOL had more than 8 million subscribers and simultaneous access for about 260,000 subscribers (Wall Street Journal, Jan.17, 1997) that yields a ratio of almost 31
subscribers per modem. This ratio was perhaps sufficient when per-hour usage charges were being assessed on AOL subscribers. However, when AOL went to flat rate pricing, this modem ratio was no longer acceptable because user behavior changed and many call requests were blocked (i.e., busy signals).
35 An example of such a distribution is the negative exponential distribution. However, the Erlang B is valid with any general distribution. Hence, the modem pool can be considered as an M/G/c/c system.
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ρ=subs×percent×hold
ErlangB(c,ρ) represents the steady state probability of all c modems being busy (a.k.a. the blocking probability).36
For the model, two Excel macros were created: ErB and ErBSlv. ErB(c, ρ) returns the blocking probability while having c modems and ρ load. ErBSlv(blockprob, ρ) returns the necessary number of modems given a blocking probability of blockprob and a load of ρ. Essentially, the ErBSlv macro tries different values for the number of modems in the ErB macro until it finds enough modems to satisfy the blocking probability. The macros and corresponding code are described in more detail in Appendix 2.
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Table 13 summarizes the values used to determine the cost and sizing of the modems.
To determine the number of required modems, the ErBSlv macro needs inputs for the blocking probability and the load.As seen in the above chart, the blocking probability is a parameter. The load needs to be calculated. Depending on user behavior, load will vary throughout the day. Normally, an ISP would size its modems according to the period of the day when the load is greatest (i.e., modem busy-hour). Because there are both
residential and business dial-in users with different demand patterns (which can be varied as input parameters), the modem busy-hour load for each POP needs to be calculated.
36 Hence, for 5000 subscribers, where 10% of them call during peak hour and the average holding time is 1 hour: ErlangB(489,500) = 0.05, which means that at least 489 modems are required so that there is no more than a 5% chance that all modems are full (blocking). The corresponding modems/subscriber ratio for this example is 10.225.
37 The list price of a US Robotics Total Control Hub of 48 modems [configured with (1) Dual T1 Card, (12) Quad Digital Modem Cards, (1) Edge Server (NT), (1) Total Control Hub (SNMP Managed), and (1)AC
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blocking probability for sizing equipment38 1.0% 1.0%
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The call arrival rate for each hour is determined:
call arr. rate = (# res. subs.) * (% res. access during hour) + (# bus. subs.) * (% bus. access during hour)
The maximum call arrival rate over a 24 hour period is what is used in the ErBSlv formula. Along with the call rate, the average holding time is used to determine the maximum load. It is assumed that the average holding time is the same for residential and business dial-in users.
The results in Table 14 are based on the number of residential and business dial-in subscribers and their call patterns.
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Costs are allocated based on total daily usage (not peak usage) between residential and business analog dial-in subscribers. Of the total number of minutes per day the analog modems are occupied, residential dial-in subscribers account for 99.6% and business dial- in subscribers account for 0.4%. This disparity is due to the large number of residential subscribers relative to the business subscribers.
Power Supply] is $51,000, which is $1062 per modem. The list price of an Ascend MAX 4004, which supports 72 analog modems (configured with chassis and [6] 12 port modem modules), is $50,000, which is
$690 per modem. An average of these prices is $875 per modem, or $42,000 for 48 modems.
38 Setting this value is subjective, based on how thoroughly the ISP wants to prevent blocking. The higher the number, the lower the total modem costs, but the higher the number of unhappy dial-in subscribers.
Sensitivity analysis is conducted on this parameter in chapter 4.
RESULTING QUANTITY BASELINE IT
leveled cost/modem/month $23 $23
Tier 1 POP modems
peak combined calls per hour 385 462
Total number of modems per POP 213 298
resulting sub/modem ratio 9.1 6.5
Tier 2 POP modems
peak combined calls per hour 1,539 1,847
Total number of modems per POP 794 1,131
resulting sub/modem ratio 9.7 6.8
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