A Simple Method for Determining an Optimal Number of Access Points in Distributed WLAN Networks

In large wireless installations based on WLAN systems, mechanisms governing their operation other than just those related to the radio coverage may play a crucial role in the customer experienced quality of service (EoS). In particular, two factors have been identified as having a particular impact on the final efficiency of the distributed WLAN network. The first one is the IEEE 802.11x protocol overhead (assisted with the choice of the preamble length) which is largely dependent on the kind of WLAN standard used – ‘b/g’, ‘a’ or ‘n’. The other factor is the MAC protocol scheme, the CSMA/CA, developed for the IEEE 802.11x family, identical for all its sub-standards. A simple formula has been developed that accounts for both these aspects and provides an easy-to-implement method allowing deployment of the minimum number of access points as a function of the expected number of users, assuring a guaranteed effective throughput per user at optimal utilization of the total available capacity. DOI: http://dx.doi.org/10.5755/j01.eee.19.9.5658


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Abstract-In large wireless installations based on WLAN systems, mechanisms governing their operation other than just those related to the radio coverage may play a crucial role in the customer experienced quality of service (EoS).In particular, two factors have been identified as having a particular impact on the final efficiency of the distributed WLAN network.The first one is the IEEE 802.11x protocol overhead (assisted with the choice of the preamble length) which is largely dependent on the kind of WLAN standard used -'b/g', 'a' or 'n'.The other factor is the MAC protocol scheme, the CSMA/CA, developed for the IEEE 802.11x family, identical for all its sub-standards.A simple formula has been developed that accounts for both these aspects and provides an easy-to-implement method allowing deployment of the minimum number of access points as a function of the expected number of users, assuring a guaranteed effective throughput per user at optimal utilization of the total available capacity.

I. INTRODUCTION
The technology addressed in the paper grounded on the IEEE 802.11x family of standards started off as a wireless extension to home local area networks; however, its usability has quickly been appreciated in other applications.Nowadays, the range of applicability reaches network connectivity services in shopping malls, airports, town squares, campuses, etc.Unlike cellular technologies that involve intensive research prior to deployment, the development of WLAN-based wide coverage networks has followed an trial-and-error path with very little theory on effective planning of such networks (let alone security aspects which are still given far too little attention by WLAN administrators).Although keeping pace with such a rampant growth of application space is an uneasy task, some efforts have been made on developing methods for optimal planning; either regarding the determination of optimal locations for a group of cooperating access points or evaluating their number based on the adaptive channel selection or the radio coverage (e.g.[1]- [7]).In this paper another aspect will be addressed associated with the Manuscript received February19, 2013; accepted June 26, 2013.throughput efficiency to be achieved with WLAN systems and its impact on the prospective number of access points (APs).As a result, an optimal number of access points will first be found and on this basis further investigations may proceed (such as propagation and channel selection issues).

II. IEEE 802.11X -GENESIS AND THE STATE OF THE ART
The WLAN (Wireless Local Area Network) systems have been present in the customer market since 1997.As the first release, i.e.IEEE 802.11 [8], did not offer impressive performance (i.e.merely 1 Mb/s -and 2 Mb/s of throughput), it was soon replaced with two other offspring: 802.11b [9] and 802.11a [10], offering the maximum data rate of up to 11 Mb/s and 54 Mb/s, respectively.In 2003 another WLAN version was released: 802.11g [11] being a 2.4 GHz equivalent in performance to its 802.11a counterpart operating in 5 GHz UNII band.In 2009 a breakthrough 802.11n [12] generation was launched with the maximum offered throughput of 600 Mb/s due to the use of some innovative techniques such as: MIMO technology (up to 4 × 4), increased number of subcarriers (now 52 compared to 48 used in previous releases), the channel width (up to 40 MHz versus former 20 MHz) together with enhanced frame-aggregation techniques improving the transmission effectiveness.The market adoption of WLAN systems has led to a veritable boom in the customers' and vendors' interest which is best expressed in the 30 % growth in the Access Points sales per yeara figure maintaining for the past few years.At present, yet another WLAN generation is being strongly promoted, although still in the draft 3.0 stage accepted in May 2012, offering data rates up to 7.2 Gb/s, with the first equipment already available for purchase.Such a momentum could not be left unnoticed by the cellular technologies carriers, vendors as well as scientific communities [13]- [25].Owing to its ubiquitous presence at the customers' premises and public institutions, WLAN is now recognized as a serious candidate serving as a technology for offloading the cellular 4 th generation LTE (Long Term Evolution) system from a significant amount of the indoor-originated user traffic.

III. ON TRAFFIC SCENARIOS IN LARGE PUBLIC SPACES
The ideas presented in this paper come from the experience acquired during deployment of WLAN systems in some public places in Poland, mainly shopping plazas where the telecom traffic generated by users shows a similar profile as that of customers visiting stores.Hence, after the site opening there is a linear growth that stabilizes at c.a. 11 a.m. and continues till evening hours (c.a.7 p.m.) to decline steadily till the facility close-up late night.In peak hours, however, the number of simultaneous users may reach up to 200 or moremostly customers in café's, fastfood bars or entertainment and meet-up sections.Since the wireless access in a commercial area is an effective attractor, an adequate quality of services must also be guaranteed to end-users.It will be reasonable, therefore, to prepare the complex system for efficient operation even during rush hours.Moreover, the system configuration must be such as to allow users nomadic access if not mobile between access points (APs).Mobility, however, still presents some problem during hand-off procedures whichso farrequire the connection with the current AP to break before authentication and/or authorization procedures with another AP take place.During this switch time some frames may be inevitably lost which may, in turn, cause some realtime applications to close sessions.To alleviate the situation a specification IEEE 802.11r has been ratified in 2008 which manages the hand-off procedures in the entire system assuring seamless roaming between APs (although no onthe-market products are known to implement it yet except firmware solutions that claim to operate just as well as the 802.11r specification).

IV. ON THE IEEE 802.11X TRANSMISSION EFFICIENCY
Users nowadays are accustomed to some level of service provided by network service providers.Albeit in public places the expectations are lower, however that which is considered as 'satisfactory' is still on the order of at least 1 Mb/s.A simple, yet unrealistic solution for a WLAN designer would consist in dividing the physical rate offered by an AP (e.g.54 Mb/s in 802.11g) by the expected data rate per client to obtain the number of users enjoying this assumed data rate.This paper will explain why such an approach is faulty and how to calculate the required number of access points in order to provide users with guaranteed data rates for their improved satisfaction.Since our investigations are best suited to wide-area scenarios, it is assumed that individual access points are spaced from each other at distances assuring non-interference operating conditions (which also assures the most efficient radio coverage).
Since IEEE 802.11x standards are only defined in the physical (PHY) and the MAC (Medium Access Control) sublayer of the ISO/OSI stack, the throughput calculated here will be one achieved "on top" of MAC, i.e. including the overhead due to the multi-access procedures but neglecting upper OSI/ISO layers.

A. The Upper OSI/ISO-layers overhead efficiency ()
As was first indicated in [26], each WLAN type bears some intrinsic features that set an upper bound on the achievable throughput (just above the MAC layer), referred to in this paper as the MAC-layer data rate RMAC1 (see also [26]- [28]).The ratio of this achievable throughput (RMAC1) related to the data rate at the physical layer (RPHY) will be termed as transmission efficiency of the first type , as given by (1).The index '1' in the subscript of RMAC1 means that only the effect of the first efficiency on the resultant RMAC will now be studied (as opposed to RMAC2 in Section IVB), remembering that in reality both efficiencies should be considered simultaneously. .
The reasons for RMAC1 being much lower than RPHY throughput are the following:  Each frame preamble is transmitted at constant data rates (i.e. 1 or 2 Mb/s as in 802.11 b/g/a) or for a defined fixed period of time (for 802.11/n).The same rule applies to the frame header.Depending on the standard the preamble duration TPRE varies from 16 s to 144 s whereas that of the PLCP header TH lies between 4 s to 48 s;  WLAN devices need to compete for access to the wireless medium.In CSMA/CA algorithmnative to IEEE 802.11x familythe transmission cycle is shown in Fig. 1.Before any transmission starts, each device waits for a DIFS (Distributed Interframe Space) period of time TDIFS equal to 2•TSLOT + TSIFS, that depending on the standard, lasts for either 28 s or 50 s.In this type of efficiency (), however, it is assumed that there are no other competitors except the investigated one;  The coding rate between 1 /2 and 5 /6.As one can see in Fig. 2 the achievable throughput is very dependent on the payload size with the maximum performance for the largest packets.In most practical situations this means packets of about 2 kB, although it is a matter of the operating systems restrictions regarding the MTU parameter (Maximum Transmit Unit).Nevertheless, even with these packet sizes the achievable data rate (RMAC1), limited by the transmission efficiency  given by (1), is only a fraction of the nominal PHY data rate RPHY, as presented in TABLE I. Equations ( 2) and (3) define RMAC1 for WLAN 'a/g' and 'n', respectively, where TSYMthe OFDM symbol duration, Lthe user data length, LACKthe acknowledgement frame length, NDBPSthe number of usable bits per OFDM symbol, NSSnumber of antennas in the MIMO scheme (see [9]- [12] for more information).
This feature, in turn, is attributed to the fact that the preamble and the PLCP header transmission as well as the multiple access procedures are only performed for a single spatial data streamall the other streams are free from this overhead and contribute to the steep increase rate for even small or moderate packets:

B. The CSMA/CA multi-access efficiency ()
The other type of efficiency () is strictly associated with the multiple access mechanism defined for WLANs.In Section IVA it was deliberately assumed that no competition exists and therefore CWmin parameter was set to the absolute possible minimum, i.e. a single Tslot.However, if many stations are competing for access to an AP, collisions may (and do) occur.If one takes place, the colliding devices double their CWmin and repeat this multiplication upon each consecutive collision occurrence until CWmin = 1023 in which case CWmin is reset to the minimum value (i.e. 15 or 31) during the next collision.Intuitively, as the number of competing stations grows, so does the probability of two or more colliding upon access attempt, which results in increased average back-off in the network during which no device is transmitting.These backoffs, in turn, cause the access point to operate even beneath its transmission capacity (or throughput performance) discussed in Section IVA.In [17] the CSMA/CA efficiency was found to exponentially depend on the number of users NUS (or WLAN cards) contending for access to the medium as shown in Fig. 4. One curve in the figure represents the simulated  whereas the other shows the best-curve approximation with R 2 = 0.993.As one can observe, even with five stations per a single AP (NUS_AP), the transmission efficiency is declines to c.a. 80 % and further down to a little above 60 % for NUS_AP = 50.It is also worth noticing that NUS_AP in fact equals NUS/NAP, where NUS is the total number of users that need to be provisioned with network services in a given site and NAP is the number of access points.

V. ESTIMATION OF THE OPTIMAL NUMBER OF APS
In the previous section two kinds of transmission efficiency were discussed.As was stated there, simply dividing RPHY by NUS will lead to a great overestimation of the user's real achievable throughput above MAC.Therefore in a general form, the MAC-layer data rate per a single user is defined as a ratio of RMAC and the number of users per AP (NUS_AP), as in (4), whereas the number of users per a single AP by (5).Finally, substituting ( 6) and ( 5) to (4) and then substituting the formula for 2 from Fig. 4 into (6) we may easily factor out the required number of access points NAP (7) necessary to provide each of the total NUS users with a guaranteed MAC throughput RUS.The simple formula allows one to quickly estimate the number of APs of a certain kind (say WLAN 'a', 'g' or 'n'), specifying on the input the total expected number of users NUS, the physical data rate RPHY offered by the APs (usually put explicitly on the product box) and the throughput RUS one wishes to guarantee the end user, above MAC layer.
For the estimation of the available data rates at higher OSI/ISO layers refer to [14] In plots shown in Fig. 5, three curves are drawn in accordance with (7), where each user's guaranteed data rate RUS is used as a parameter.For instance, with NUS = 200 users, five APs are necessary to provide RMAC of 0.5 Mb/s whereas providing RMAC of 1.5 Mb/s would require twelve APs.

VI. CONCLUSIONS
Two sources of reduced user throughput (above MAC) in WLANs were analyzed and treated as efficiencies: one occurs due to the constant lag caused by the protocol overhead and the other due to the CSMA/CA contention protocol.Their combination allowed the authors to derive a concise formula for the necessary number of access points required to assure a fixed level of throughput to each user (out of all NUS users), which may be of easy use to WLAN designers at commercial sites.

Fig. 4 .
Fig. 4. CSMA/CA transmission efficiency vs. the number of users per AP.

Fig. 5 .
Fig. 5. Optimal number of APs vs. the total number of users and the guaranteed throughput above MAC layer.

TABLE I .
WLAN TRANSMISSION EFFICIENCY.
for example: