Jean Campbell's husband John went to look for her after she failed to return home and found her body.
The 53-year-old was discovered in Cranhill Park just yards from her home on Saturday morning. Her German Shepherd was found alive.
Police have stepped up their hunt for clues and have been trying to find a motive for the killing of the mother-of-two.
Around a dozen officers remained at the scene yesterday, guarding the park, and forensic experts were carrying out investigations. A post-mortem examination of Mrs Campbell's body has taken place.
Neighbours have told of their shock after the mother-of-two was murdered.
However, some have been concerned about their safety in the park in Bellrock Street and many have refused to use it.
It has emerged that calls have been made for improved lighting and increased CCTV in the park grounds after the killing.
An online petition calling for these changes has already received more than 420 signatures of support.
In September 2011, a 49-year-old woman was robbed and sexually assaulted as she walked to work.
A man pushed her to the ground and hit her while removing her jewellery and handbag, then sexually assaulted her before running off.
Police have put on extra patrols in the area in an attempt to reassure residents.
One woman, who did not wish to be named, said: "It makes you think twice about going out at night.
"The park definitely needs to have better lighting, you don't know who is about.
"This just proves that. It's very frightening."
A Glasgow City Council spokesman said: "This is a shocking and tragic incident.
"However, it is important that people remember that crime levels in our parks are relatively low.
"The council will continue to work with Police Scotland, Community Safety Glasgow and other partner agencies, to tackle all forms of crime."
Detectives have been speaking to her neighbours in an attempt to piece together Mrs Campbell's final movements.
Police patrols are being stepped up in the area after her body was found at around 7.40am on Saturday.
Extra high-visibility patrols have been deployed around the park in a bid to reassure concerned local residents.
Forensic experts, in white suits, were seen working in Cranhill Park and a protective white tent had been erected.
Mrs Campbell was last seen by a family member at about 5pm on Friday.
She left her flat in Bellrock Street, which is near her home, to walk her German Shepherd. Police Scotland said a post-mortem has taken place and police are now treating her death as murder.
Officers are carrying out door to door enquiries in the local area and checking CCTV footage.
Detective Chief Inspector Colin Carey, who is leading the investigation, said "extensive inquiries" are under way.
He added: "I would urge anyone who saw her between 5pm on Friday and Saturday morning to come forward.
"Her German Shepherd-type dog was with her in the park, so we are trying to establish when she left her house to take the dog for a walk."
Her body was found in the park close to the Cranhill Beacon Play Centre, an activity facility for five to 12 year olds in the area.
Mrs Campbell has been described by friends as a quiet woman was well-known and liked within the community.
One local resident said that she was always seen out with her dog.
Her family have not yet commented.
Anyone with information is asked to contact police on 101.