Your question seems awkwardly worded. I am pretty sure you mean connecting the telephone system to a wireless device, as opposed to running your IP PBX off of a wireless network. The former is definitely possible, but I'm not sure about the latter. I'm not aware of enterprises running their phone systems entirely off of mobility, and I highly doubt it's all that feasible.
However, extending the local area network (LAN) to mobile devices makes a lot of sense, especially for employees who regularly on the go, such as those in sales or technical service. One term commonly used to describe the underlying technology here is fixed-mobile convergence (FMC). As the name implies, these types of solutions enable a seamless handoff of calls from the wireline network, where the IP PBX is rooted, to a wireless network, which is what your mobile device works from. These networks are different and not natively compatible, which is why we have FMC solutions. They make it possible to transfer calls between networks on the fly, such as when you're on the IP PBX, and you have to leave the office. FMC allows you to continue the call on your mobile device as you're leaving, without having to drop the landline and re-connect on your cell phone.
In terms of reliability, these calls can be very reliable if routed over a 3G network. Not all mobile carriers support FMC yet, but for those that do, their networks are usually large enough to support most of these needs. FMC calls can also be routed over Wi-Fi, but these networks are less reliable as well as less secure. Wi-Fi coverage is much less widespread than 3G, so this option is more variable, and really depends on local availability as an option for FMC.
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