Estimating the cost of SMS

Marginal cost analysis

One way to estimate the cost of an SMS is to look at the price per SMS in a bundled plan. For instance, according to T Mobile's response to Sen. Kohl (http://kohl.senate.gov/TMobile%20100308.pdf), T-Mobile, AT&T, and Sprint all offer a plan (such as 1000 messages for $10) where the cost of an SMS is 1 cent. Assuming that they would not want to make a loss, this upper-bounds the cost of an SMS to 1 cent.

One could argue that this analysis is simple-minded, in that it assumes that a person who subscribes to, say, a 400-message plan would actually send 400 messages. In reality, they may only send 200 or 300. Given sufficient statistics, it would be possible to price a plan for this mean rather than the maximum and still make money.

To counter this, we can take into account first order price discrimination. More simply put, all this means is that a person who has a choice of, say, a 400 message plan and an unlimited message plan would choose the unlimited message plan only if they sent at least 400 messages. So, if we were to divide the cost of unlimited messages by 400, we have a tight upper bound on costs.

T Mobile charges $15 for unlimited messages and the next lower tier is 1000 messages, so the tight upper bound is 1.5 cents. Similarly, AT&T charges $20 for unlimited messages and the next lower tier has 1500 messages, which gives a bound of 1.33 cents. The equivalent cost for Sprint is 2 cents and Rogers is 8 cents. Other than Rogers, which is an outlier, this analysis shows that the cost of an SMS is at most about 1.5 cents.

Channel costs

We can get a better handle on the costs of an SMS from first principles.

SMS is sent over a control channel (the Standalone dedicated control channel SDCCH (http://wireless.agilent.com/rfcomms/refdocs/gsmgprs/gen_bse_dcch.php)) that is also used for call control and signaling. Because logical control channels can be overlaid on any underlying physical channel, if the SMS volume grows, it is possible to allocate additional SDCCHs to carry SMS messages: this simply displaces a Traffic Channel (TCH) that would otherwise be used for voice. We can use this observation to compute the cost of SMS as follows:

Voice is carried in GSM as a 8kbps stream, that is, 8000 bits/second. A SMS is 140 bytes or about 1100 bits. Therefore, a physical channel can carry 7 SMS messages/second, or 420/minute. Of course, this assumes 100% utilization. But the SDCCH is a slotted Aloha system, which saturates at about 37% utilization. So, let us say we conservatively operate the channel at 20% utilization. This gives us a capacity of 84 SMS/minute.

The price of a voice minute in Canada is about 15 cents/minute as overage but only about 10/cents/minute as part of a plan (http://www.your.rogers.com/business/wireless/plans_services/business_plans.asp?shopperID=BFXLRL48CR9A9LHF8DX6F1NLPKE3BJUE&plan=cor&cat=1&typ=2). (A report from Merrill Lynch estimates that the mean cost per voice minute in 2007 was 11 cents in Canada. Elsewhere, the price varied from a global high of 32 cents a minute in Switzerland to a global low of roughly 2 cents a minute in Bangladesh and India.) The per-minute cost of a physical channel is upper bounded by this price. So, the channel cost of a SMS can be upper-bounded by roughly 10c/84 ~= 0.10 cents.

Billing costs

Each SMS can result in one or more messages being sent to a billing system. I have no way to estimate the cost of these messages. One way to bound this cost is that carriers clearly will not make a loss when pricing SMS (as part of a plan) at roughly 1.5 cents/SMS. Based on my computation that the channel cost is 0.1 cents, the messaging cost cannot exceed 1.4 cents. If this is indeed the accounting cost, operators make no money on SMS as part of a plan but 13.5-18.5 cents/SMS for out-of-plan messages.

However, I find it hard to believe that accounting for an SMS (monitoring, finding what rate plan it should be charged at, and then adding it to a customer's bill) would cost fourteen times as much as carrying the SMS itself. If we assume that accounting is twice as expensive as carrying an SMS, then we can estimate the cost of an SMS at 0.3 cents, which is much lower than the marginal cost analysis result of 1.5 cents.

Without a plan, carriers charge 15-20 cents/SMS, and with a plan, about 1.5 cents/SMS. So, even with a plan, carriers have a greater than 90% margin. No wonder SMS accounts for $100billion in revenue worldwide (http://www.communities-dominate.blogs.com/brands/2008/12/trillion-with-a.html).

Accounting for paging costs

If the location of a mobile is not known, the paging channel is used to locate it. Essentially, a paging message is sent to all the cells where a mobile could possibly be located and the mobile answers the paging message, making itself known. The recipient of an SMS, therefore, causes paging load on the operator which adds to the operator's cost. A correspondent wrote to me stating that my calculations do not include this cost.

This criticism is valid. In the calculation above, I made the simplifying assumption that the location of the phone was known, and that a physical channel was being used either for voice or SMS (or, to be precise TCH or SDCCH). It is difficult to estimate the true cost of signaling because every operator can choose a different paging policy. For instance, with aggressive location tracking, every handoff will result in an update to the VLR, but then there is no need to page. This works well for relatively static mobile phones. With less aggressive location tracking, all cells near the last known cell need to be paged. This reduces the tracking costs for highly mobile phones, but increases paging costs. How should this be accounted for?

Note, however, that paging traffic is necessary even for call establishment, and presumably has already been rolled into the cost of a voice minute. One way to do so would be to assume the mean call length to be, say, 3 minutes, and dividing the number of minutes in a plan by this to obtain the number of pages expected. Then, the per minute cost would (or, at least, should) include the paging cost as well, and this is the cost I am comparing with.

Of course, a three-minute call has only one page, and one could argue that each SMS requires a page. Thus, it would appear that SMS has much higher paging overheads. Again this argument is false: once a mobile has been located, either for a call or an SMS, it no longer needs to be paged. So, the paging costs for a call or an SMS are comparable. They would not be comparable only if some mobiles were very much more likely to use SMS compared to making or receiving a voice call. My guess is that an active mobile would be both making/receiving calls as well as SMSs, so this is not likely to be the case.

SMS volumes

• The number of text messages in 2008 is likely to be 2 trillion (according to Gartner): http://www.gartner.com/it/page.jsp?id=565124

• The message volume for 2 trillion messages = 140 bytes * 8 bits/byte * 2* 10^12 = 2,240,000,000,000,000 bits = 2.24*10^15 bits. A 10 gigabit line carries 10*10^9 bits/sec = 10^10 bits/sec. So, to carry the entire message volume will take 2.24*10^5 seconds = 224,000 seconds = 62 hours. But a year has 365*24 hours, so that on average a 10 gigabit trunk line would be actually 0.7% used by sending 2 trillion SMSs (leaving 99.3% available for other traffic). Note that Verizon actually sells 10Gbps service to its customers:http://www22.verizon.com/wholesale/solutions/solution/U.S.%2BWavelength.html So, its own trunks are likely to be even higher capacity. Thus, going from a million to a 100 million messages does not really add much to a carrier's load on its backbone -- even a load of 2 trillion messages only occupies 0.7% of a backbone link!

• Sending a million messages a year corresponds to sending 114 SMSs an hour or 1.9 SMSs a minute. If 100 million messages are sent in a year, this amounts to 190 SMSs/minute. Recall that a single voice channel can carry roughly 84 SMS/minute. So, if the SMS volume goes up by a factor of 100, the operator has to go from allocating one TCH to SMS to three. But in each GSM cell, an operator has roughly 1000 voice channels. Thus, going from 1 million to 100 million SMSs does not add much to a carrier's load on its wireless spectrum.

• Taking these two facts into account, it appears that going from 1 million to 100 million SMSs does not greatly strain a carrier's infrastructure.

• The cost of storage is dropping fast. Today, consumers can buy 1TB, which is enough for 7.1 millions SMS messages for about $100 (http://www.pricegrabber.ca/search_attrib.php/page_id=11/form_keyword=1tb%20drive/rd=1/mode=g_ca_b_s/skd=1/st=query). If you want RAID 5 with striping, its a little more expensive, about $1000/TB (http://www.pricegrabber.ca/search_getprod.php/masterid=37892089/). With open-source clustered file systems, such as Gluster (http://www.zresearch.com) there is no need for expensive top-of-the-line SAN/NAS solutions, either.