Share or not share capacity? Target customer type in batch service queue systems

This study examines the behaviour of two service companies under the M/M[n]/1 batch service queueing model, which divides their customers into brand-loyal and searching categories. Our research indicates that when market conditions are highly competitive and the rewards for different types of customers are similar, these firms primarily cater to brand-loyal customers in very large or very small markets. However, when the market is moderate, they expand their customer base to include all types. It is worth noting that as the difference in rewards between customer groups increases, these firms focus exclusively on brand-loyal customers. In co-opetition, where both companies provide similar services, they aggressively cut prices to attract searching customers. This fierce price competition ultimately drives prices down to marginal cost levels, eliminating the possibility of profit and compelling a strategic pivot back to prioritizing brand-loyal customers. Our research indicates that under co-opetition, firms are more likely to achieve higher revenues in extremely large or small markets. In contrast, in competitive settings, firms tend to secure greater profitability in markets that maintain specific proportions of brand-loyal customers.