Much-needed supplies and a third tugboat are heading across the Gulf of Mexico to try to make the end of the miserable voyage of the Carnival Triumph as comfortable as possible for hungry travelers who have waited in lines for hours for food and other necessities.

Carnival Cruise Lines said Wednesday afternoon it has dispatched another tugboat to help two others tow the disabled and befouled cruise ship to port in Mobile, Alabama, with U.S. Coast Guard escorts on the scene.

The cruise line also said it would compensate passengers $500 each in addition to measures previously announced, including refunds.

Carnival said on its Facebook page that it decided against sending another ship to pick up passengers because towing the ship to port was the safest option.

The Coast Guard delivered equipment to the struggling ship Wednesday afternoon, including a generator and electric cables.

Nerves are frayed on board, where passengers have waited in lines for as long as four hours, said Nick Ware, whose mother is on the ship with her boyfriend. Ware said arguments are breaking out after people at the front of lines grab as many provisions as they can.

"The person in the front of the line is allowed to take however much he wants, so people see the person in front of them taking too much, (and) they start to get concerned they're not going to get any," Ware said.

People at the rear of the line ended up with buns and condiments -- no burgers, he said.

Meanwhile, on shore, Kim McKerreghan stood in the dark at dockside in the Port of Mobile early Wednesday, worried about her 10-year-old daughter and her ex-husband, both passengers on the distressed cruise ship.

Her daughter, Allie Taylor, called her in a panic Sunday after a fire broke out in the Carnival Triumph's engine room.

Automatic sprinklers extinguished the blaze, but the flames paralyzed the ship's propulsion system, leaving it temporarily marooned in the Gulf of Mexico, subject to the whims of wind and sea currents.

"Mommy, it's so scary," McKerreghan said her daughter told her. "I want to come home." McKerreghan fought back tears as she recalled the conversation. "Just come get me," her daughter begged her.

The cell phone signal was bad, and they ended the call, leaving the mother from Lufkin, Texas, feeling helpless. "I wanted to have a meltdown," McKerreghan said. "I'm going to have that moment here," she told CNN's Victor Blackwell at the Alabama port.

Ware said he has been told that some of the public restrooms work, meaning that people waiting in those lines can stop using red biohazard bags for waste.

Slow trip home

For most of the day Wednesday, two tugboats dragged the nearly 900-foot, 14-story Triumph at a jogger's pace to the harbor, where the 3,143 passengers and 1,086 crew members on board will get off the vessel on Thursday, the cruise line said.

The convoy was approximately 108 nautical miles (about 124 statute miles) from port around 5 p.m. ET Wednesday, the Coast Guard said. The ship is on track to arrive at the Mobile dock around 4 p.m. ET Thursday, an official briefed on plans for the recovery of the ship said.

The Triumph is expected to navigate the "safety fairway," or the corridor into Mobile Bay, late Wednesday night, bringing it around 10 a.m. Thursday to the point where a pilot from the Port of Mobile will board the ship and guide it to dock, the same official said.

Mobile Infirmary Health Services has offered to set up a triage unit at the port, in case any debarking passengers need medical assistance, Alabama Cruise Terminal General Manager Sheila Gurganus said Tuesday.

Then, after what Gurganus predicted would be "easy access out the door of customs with your luggage," about 200 Carnival employees will try to take care of its passengers on land.

"We are currently finalizing travel arrangements for guests from Mobile. Carnival Triumph guests were given the option of boarding buses directly to Galveston or Houston, Texas, or to spend the night in a hotel in New Orleans, where they could rest before flying out on private charters the next day. Carnival will cover all travel-related and incidental expenses," the cruise line said.

Carnival said it has reserved and arranged approximately 100 motor coaches, more than 1,500 New Orleans hotel rooms, multiple charter flights from New Orleans to Houston on Friday and transportation from Houston to the Port of Galveston so that guests may retrieve their cars if they drove to the port.

'It's disgusting'

The cruise ship left Galveston for a Caribbean tour last week and was scheduled to arrive back there Monday.

That day, McKerreghan's ex-husband, stranded at sea, phoned to say the sanitary situation had already begun to deteriorate on board the Triumph.

"He said that the conditions have gotten so bad that they're asking them to use the restroom in bags, and they were eating onion sandwiches," McKerreghan said.

The call was the last she has heard from them.

Much of the ship's electrical power went down in the fire, causing widespread malfunctions, including taking out sanitary systems.

Passengers have reported sewage sloshing around in hallways, flooded rooms and trouble getting enough to eat.

"It's disgusting. It's the worst thing ever," passenger Ann Barlow said.

"From what I understand, they're walking around in a lot of urine and fecal matter, and the sewers are backing up," McKerreghan said. Her doctor gave her antibiotics to give her daughter as soon as she gets on land. A checkup will follow as soon as possible.

Passenger Jet Hilton from Crawfordsville, Indiana, has relied on her sense of humor to get through the ordeal, her sister Jennifer Stanfield told CNN affiliate WTHR.

Four-thousand people on a stranded ship can't flush, Hilton jokingly messaged Stanfield, venting about the stench on board.

Other inconveniences

Hilton and 20 of her girlfriends booked the cruise to celebrate one of their birthdays.

She is a former cheerleader, Stanfield said, and is doing what she can to keep her group's spirits up.

The fire also cut power to air conditioning, and the ship is very hot, Stanfield said. Passengers are flocking to the deck for fresher, cooler air.

The crew has higher priorities to fulfill than cooling cabins with what electricity the ship does have.

"They have to make sure there's adequate power to keep the ship from sinking or burning further," said Dr. Richard Burke from the University of New York Maritime College.

The fire also knocked out the ship's stabilization system, causing it to list, Burke said.