queue theory

introduction

whenever demand exceeds capacity in a given time period, a backlog will develop resulting in a wait queue
it is thus important to try to match capacity to demand over the time periods
- eg. ED doctor staffing and assessment spaces and discharge capacity vs patient arrivals by hour of day
all serial systems will have at least one rate limiting process (constraint) which produces a bottleneck, and the strength of a serial process is limited by the weakest link in the chain
it is critical to discover the bottlenecks as throwing resources at other areas will be wasteful and not improve flow whilst a residual bottleneck causes critical constraints
one can use process mapping and root cause analysis methods to determine such bottlenecks
demand can be measured by number of patients arriving x average amount of time to process them to discharge
capacity can be measured by max. number of patients that can be processed x average amount of time to process them to discharge
unfortunately ED systems are quite complex and mathematical models are not as simple as one would like
furthermore, Economics 101 theory means that if you increase capacity and reduce the cost (time or money cost) to patients or ambulance service in the process, demand will increase as service shifts from higher cost services

process mapping the ED patient

triage
- basic demographic details
- why are they here?
- brief clinical assessment
- assign urgency priority to assist safe queue management
- allocate to stream/team/location
clerking
move to appropriate assessment cubicle when available
assign to doctor
clinical assessment and re-assessments:
- assessment by Dr +/- nurse
  - +/- collect collaborative information from LMO, family, pathology/radiology providers
- access clinical decision support systems
  - senior ED doctor
  - care coordinators
  - ED mental health teams
  - inpatient unit doctor
  - clinical guidelines
  - internet search
- clinical documentation
+/- order and administer medications and iv fluids in ED
+/- order investigations:
- bed-side tests:
  - urinalysis
  - urine pregnancy tests
  - blood glucose
  - blood gas analysis
  - bedside ED ultrasound
- pathology tests:
  - order request
  - blood sampling, LP or urine collection and labelling of specimens
  - transport specimens to lab
  - lab processing and reporting of results
  - iterative checking for availability of results by Dr
  - assessment of results
  - potential “add-on” additional tests
- radiology tests:
  - obtain permission for test - ED senior, radiology registrar
  - order request
  - +/- 1hr of oral contrast for abdominal CT scans
  - transport patient to radiology +/- orderly, nurse, monitoring equipment, Dr
  - radiology processing +/- ED Dr to administer iv contrast
  - placement of images on PAC system
  - iterative checking for availability of images by Dr
  - assessment of results +/- contact radiology registrar for formal report
  - potential additional radiology
- emergent MRI scan:
  - initial assessment of patient suitability - contra-indications to MRI, etc
    - patients with coronary stent will need to have details of device(s) from the treating hospital(s)
    - some patients may need plain imaging if concern of old metal in-situ
  - obtain permission for test:
    - ED senior, subspecialty registrar (eg. oncology, neurosurgery)
      - may need to arrange digital transfer of existing images to tertiary centres
    - radiology registrar or MRI consultant
  - order request
  - +/- liaise with MRI tech to decide upon C/I issues - eg. specific type of in-situ stent
  - transport patient to MRI +/- orderly, nurse, monitoring equipment
  - radiology processing and placement of images on PAC system
  - iterative checking for availability of images by Dr
  - may need to arrange digital transfer of MRI images to tertiary centres
  - assessment of results +/- contact radiology registrar for formal report
ED clinical care:
- communicate with patient, family, ED and inpatient care teams
- +/- resuscitation
- +/- wound repair
- +/- dislocation/fracture reduction
- +/- plaster application
- +/- review by inpatient team
- etc
discharge process:
- discharge home or residential care:
  - +/- safety check for discharge home by care coordinators
  - +/- contact family or residential care facility to ensure suitability
  - +/- arrange transfer
  - +/- arrange follow up mechanism
  - discharge letter including process for LMO to follow up results
  - prescription
    - +/- medication approval systems - hospital vs PBS
    - +/- ED dispensing after hours
  - patient education
  - sick certificate
  - find and print patient information sheet
  - discharge
  - discharge patient from IT system
- admit to hospital:
  - +/- contact family to ensure suitability
  - contact inpatient team to accept admission
    - +/- request for further investigation prior to acceptance
  - place bed request into system
  - await bed allocation
  - +/- await admission by inpatient team
  - +/- await patient stability
  - +/- complete interim admission orders
    - usual medications written up
    - iv fluid chart
    - instructions for ward nurses
  - +/- arrange transfer to another hospital
  - discharge to ward +/- orderly, nurse
  - discharge patient from IT system
clean assessment room