Optimising resources in healthcare facilities is essential for departments to cope with the growing population's requirements. An aspect of such performance modelling involves investigating length of stay, which is a key performance indicator. Stroke disease costs the United Kingdom economy seven billion pounds a year and stroke patients are known to occupy long periods of time in acute and long term beds in hospital as well as requiring support from social services. This may be viewed as an inefficient use of resources. Thrombolysis is a therapy which uses a clot-dispersing drug which is known to decrease the institutionalisation of eligible stroke patients if administered 3 h after incident but it is costly to administer to patients. In this paper we model the cost of treating stroke patients within a healthcare facility using a mixture of Coxian phase type model with multiple absorbing states. We also discuss the potential benefits of increasing the usage of thrombolysis and if these benefits balance the expense of administering the drug.