Hi - As Gail stated, it is very difficult to say which is the culprit, without completely knowing your system.
Few things that can be checked - total physical memory, RAID details, data file and log files location, tempdb location, number of cpu, max memory setting, Virtual memory size, max degree of parallelism etc,.
I'll share my recent experience on working with similar kind of issue, Try it - if it is helpful.
There are two instances on a server, one is OLTP and the another is OLAP. Total RAM size is 64 GB, RAID 5+ 1 subsystem is used. 16 core processor. PAGEIO_LATCH were huge.
I checked the RAM usage, and enabled various counters for monitoring Disk usage, Memory usage etc. Observed a huge paging activity - then I found Virtual memory was configured 4 GB only (Gail only showed me some light on the dark area - Thanks again to Gail). It was increased to 110 GB. Then I collected the user queries through trace for a span of time - they were drilled down, checked its execution plan and found some issues like missing indexes, some queries were not properly picking the indexes/ right indexes. Everything was fixed, took almost 10 days. Then statistics was updated, then it started to work like a charm. Now PAGEIO_LATCH count is very very less.
Most of the time index would be the culprit hence check it. Try to create a base for your server. From that try to figure out which goes wrong.