On A Single Server Queue with Two-Stage First Essential Service Followed by One of the Two Types of Additional Optional Service and Optional Deterministic Server Vacations

We study the steady state behavior of a batch arrival single server queue in which the first service consisting of two stages with general service times G1 and G2 is compulsory. After completion of the two stages of the first essential service, a customer has the option of choosing one of the two types of additional service with respective general service times G1 and G2 . Just after completing both stages of first essential service with or without one of the two types of additional optional service, the server has the choice of taking an optional deterministic vacation of fixed (constant) length of time. We obtain steady state probability generating functions for the queue size for various states of the system at a random epoch of time in explicit and closed forms. The steady state results of some interesting special cases have been derived from the main results.

Equitable Virtual Care in Canada: Addressing The Digital Divide

Online healthcare services are rapidly transforming the landscape of healthcare in Canada. Although the digitization of healthcare delivery has been occurring gradually over the past two decades, the COVID-19 pandemic has catalyzed a “digital boom” in healthcare [1–4]. Now more than ever, healthcare practitioners and patients alike have transitioned from in-person appointments to virtual care via online platforms [3-5]. Virtual care, once an optional service, is becoming an essential one. A recent survey conducted by the Canadian Medical Association (CMA) aiming to assess Canadians’ opinions about virtual care, reported that 19% of Canadians accessed routine healthcare via phone, telehealth, virtual service, or video conference with their physician(s) prior to the COVID-19 pandemic compared to 53% since the beginning of the pandemic [5]. Due to necessity, virtual care evidently went from being uncommon to the status quo during the COVID-19 pandemic.

Analysis of Interconnected Arrivals on Queueing-Inventory System with Two Multi-Server Service Channels and One Retrial Facility

Present-day queuing inventory systems (QIS) do not utilize two multi-server service channels. We proposed two multi-server service channels referred to as T1S (Type 1 n-identical multi-server) and T2S (Type 2 m-identical multi-server). It includes an optional interconnected service connection between T1S and T2S, which has a finite queue of size N. An arriving customer either uses the inventory (basic service or main service) for their demand, whom we call T1, or simply uses the service only, whom we call T2. Customer T1 will utilize the server T1S, while customer T2 will utilize the server T2S, and T1 can also get the second optional service after completing their main service. If there is a free server with a positive inventory, there is a chance that T1 customers may go to an infinite orbit whenever they find that either all the servers are busy or no sufficient stock. The orbital customer can request for T1S service under the classical retrial policy. Q(=S−s) items are replaced into the inventory whenever it falls into the reorder level s such that the inequality always holds n<s. We use the standard (s,Q) ordering policy to replace items into the inventory. By varying S and s, we investigate to find the optimal cost value using stationary probability vector ϕ. We used the Neuts Matrix geometric approach to derive the stability condition and steady-state analysis with R-matrix to find ϕ. Then, we perform the waiting time analysis for both T1 and T2 customers using Laplace transform technique. Further, we computed the necessary system characteristics and presented sufficient numerical results.