I hate mats......... I hate cleaning them, and once clean, they have to be dry (ie hung up or draped over something for a few hours) before they go back on the floor-- or bad things happen.Whatever you do, DO NOT get the perforated style of mat, where crud gets lodged in the perforations, they are a (deleted) to get clean. In retrospect, I'd rather scoop dog crap into bags than handle floor mats
Tile floors get slippery for a number of reasons:
1) On the line, grease and oil get spilled, sauces get spilled. Fair enough. Best solution I've ever encountered for this is duck boards. Think of wooden pallets on the floor. Except these are maybe 4 ft wide and maybe 6 ft long, maybe an inch or two off the floor, and enough of them to fit behind the line. Stuff gets spilled, if falls between the wood slats, you stay dry. If the slats are greasy or slippery during service, you take a cheap corn broom and sweep the stuff down the cracks. Once or twice a day the boards are propped up, floors swept and mopped, and the boards put down again.
2) Dishpit. If the pre-rinse table and sink aren't big enough, or the landing table for the clean d/racks isn't sufficient, you get wet floors. DIsh/w has got to rattle/shake excess water from the racks while still in the machine before he takes them off the landing table. Failure to do this means water dripping all over the floor. Bar tenders are notorious for this when they do a few racks and haul them off back to the bar. Another reason is if the dish/w gets too enthusiastic with the spray gun, or the area around the spay gun isn't properly shielded. A well designed dishpit shouldn't have wet floors, and if a well designed dish pit does, the dish/w needs to be trained on how to keep it dry. For kitchens with sh*tty designed dish pits, the best retrofit is again, duck boards.
One of the big differences between European kitchens and N. American kitchens is the way they mop floors. The Euros don't. They have floor drains. Cleaning a floor there entails sweeping, hosing down the floor, scrubbing it down with scrub-brushes on broomsticks, and then taking a giant squeegee-on-a-broomstick and pushing all the water down the floor drains. Any spills during service, and you grab the giant squeegee, push it down the floor drain, and get back to work. For places that do use a mop, the floors should be dry within a few minutes of mopping--that is, when you mop, you slosh water over an area with the mop, loosening up dirt, then you wring the mop dry, and suck up the excess with the dry mop, then move on to a new patch. I was shown this technique at my very first job--at Mickey D's where it was done with two people, a wet-mopper, and a dry mopper, but can easily be done with one person and one bucket and mop..
Hope this helps.......